Professor Jie   Du
Professor

Professor Jie Du

Science
Sch of Mathematics & Statistic

Jie Du is an Associate Professor in the School of Mathematics and Statistics.

 

RESEARCH INTERESTS

A/Prof Du is a member of the School's Algebra and Number Theory and Combinatorics research groups. His interests lie in the representation theories on algebraic and quantum groups, finite groups of Lie type, finite dimensional algebras, and related topics. His recent work has concentrated mainly on the Ringel-Hall approach to quantum groups and q-Schur and generalised q-Schur algebras and their associated monomial and canonical basis theory. He is also interested in combinatorics arising from generalised symmetric groups, Kazhdan-Lusztig cells and representations of finite algebras.

Phone
9385 7087
Location
School of Mathematics and Statistics University of New South Wales Sydney NSW 2052 The Red Centre Room RC-4113

Publications

  • Books | 2012
    Professor Jie Du
    Deng B; Du J; Fu Q, 2012, A Double Hall Algebra Approach to Affine Quantum Schur-Weyl Theory, Original, Cambridge University Press, UK
    Book Chapters | 2010
    Professor Jie Du
    Du J; Fu Q, 2010, 'Quantum gln, q-Schur algebras and their infinite/infinitesimal counterparts', in Gyoja A; Nakajima H; Shinoda K; Shoji T; Tanisaki T (ed.), Representation Theory of Algebraic Groups and Quantum Groups, Birkhauser, New York, pp. 93 - 119, http://dx.doi.org/10.1007/978-0-8176-4697-4_5
    Books | 2008
    Professor Jie Du
    Deng B; Du J; Parshall B; Wang J, 2008, Finite Dimensional Algebras and Quantum Groups, Original, American Mathematical Society, USA
  • Journal articles | 2020
    Professor Jie Du
    Du J; Lin Y; Zhou Z, 2020, 'Polynomial super representations of U-q(res) (gl(m vertical bar n)) at roots of unity', JOURNAL OF ALGEBRAIC COMBINATORICS, vol. 51, pp. 195 - 235, http://dx.doi.org/10.1007/s10801-019-00872-z
    Journal articles | 2020
    Professor Jie Du
    Du JIE; Gu H; Zhou Z, 2020, 'MULTIPLICATION FORMULAS and SEMISIMPLICITY for q-SCHUR SUPERALGEBRAS', Nagoya Mathematical Journal, vol. 237, pp. 98 - 126, http://dx.doi.org/10.1017/nmj.2018.12
    Journal articles | 2020
    Professor Jie Du
    Du J; Zhou Z, 2020, 'The regular representation of Uυ(Glm', Proceedings of the American Mathematical Society, vol. 148, pp. 111 - 124, http://dx.doi.org/10.1090/proc/14688
    Journal articles | 2019
    Professor Jie Du
    Du J; Fu Q, 2019, 'The Integral Quantum Loop Algebra of gln', International Mathematics Research Notices, vol. 2019, pp. 6179 - 6215, http://dx.doi.org/10.1093/imrn/rnx300
    Journal articles | 2019
    Professor Jie Du
    Deng B; Du J; Yang G, 2019, 'Slim cyclotomic q-Schur algebras', Journal of Algebra, vol. 535, pp. 365 - 406, http://dx.doi.org/10.1016/j.jalgebra.2019.06.024
    Journal articles | 2019
    Professor Jie Du
    Du J; Lin Y; Zhou Z, 2019, 'Polynomial super representations of Uqres(glm', Journal of Algebraic Combinatorics, http://dx.doi.org/10.1007/s10801-019-00872-z
    Journal articles | 2018
    Professor Jie Du
    Du J; Parshall BJ; Scott LL, 2018, 'Local and global methods in representations of Hecke algebras', Science China Mathematics, vol. 61, pp. 207 - 226, http://dx.doi.org/10.1007/s11425-017-9171-2
    Journal articles | 2018
    Professor Jie Du
    Du J; Zhao Z, 2018, 'Multiplication formulas and canonical bases for Quantum Affine Gln', Canadian Journal of Mathematics, vol. 70, pp. 773 - 803, http://dx.doi.org/10.4153/CJM-2017-009-4
    Journal articles | 2018
    Professor Jie Du
    Du J; Wan J, 2018, 'The queer q-Schur superalgebra', Journal of the Australian Mathematical Society, vol. 105, pp. 316 - 346, http://dx.doi.org/10.1017/S1446788717000337
    Journal articles | 2018
    Professor Jie Du
    Du J; Haixia G, 2018, 'q-Schur superalgebras', SCIENTIA SINICA Mathematica, vol. 48, pp. 1571 - 1571, http://dx.doi.org/10.1360/n012017-00265
    Journal articles | 2017
    Professor Jie Du
    Du J; Gu H; Wang J, 2017, 'Representations of q-Schur superalgebras in positive characteristics', Journal of Algebra, vol. 481, pp. 393 - 419, http://dx.doi.org/10.1016/j.jalgebra.2017.02.033
    Journal articles | 2017
    Professor Jie Du
    Du J; Parshall BJ; Scott LL, 2017, 'Stratifying endomorphism algebras using exact categories', Journal of Algebra, vol. 475, pp. 229 - 250, http://dx.doi.org/10.1016/j.jalgebra.2016.11.002
    Journal articles | 2017
    Professor Jie Du
    Du J; Jensen BT; Su X, 2017, 'Presenting Hecke endomorphism algebras by Hasse quivers with relations', Journal of Pure and Applied Algebra, vol. 221, pp. 883 - 907, http://dx.doi.org/10.1016/j.jpaa.2016.08.010
    Journal articles | 2017
    Professor Jie Du
    Du J; Parshall BJ; Scott LL, 2017, 'Stratifying endomorphism algebras using exact categories', JOURNAL OF ALGEBRA, vol. 475, pp. 229 - 250, http://dx.doi.org/10.1016/j.jalgebra.2016.11.002
    Journal articles | 2016
    Professor Jie Du
    Du J; Fu Q, 2016, 'Small Representations for Affine q-Schur Algebras', Algebras and Representation Theory, vol. 19, pp. 355 - 376, http://dx.doi.org/10.1007/s10468-015-9577-0
    Journal articles | 2015
    Professor Jie Du
    Du J; Wan J, 2015, 'Presenting queer Schur Superalgebras', International Mathematics Research Notices, vol. 2015, pp. 2210 - 2272, http://dx.doi.org/10.1093/imrn/rnt262
    Journal articles | 2015
    Professor Jie Du
    Du J; Parshall BJ; Scott LL, 2015, 'Extending hecke endomorphism algebras', Pacific Journal of Mathematics, vol. 279, pp. 229 - 254, http://dx.doi.org/10.2140/pjm.2015.279.229
    Journal articles | 2015
    Professor Jie Du
    Du J; Gu H, 2015, 'Canonical bases for the quantum supergroups U(glm', Mathematische Zeitschrift, vol. 281, pp. 631 - 660, http://dx.doi.org/10.1007/s00209-015-1499-3
    Journal articles | 2015
    Professor Jie Du
    Du J; Fu Q, 2015, 'Quantum affine gln via Hecke algebras', Advances in Mathematics, vol. 282, pp. 23 - 46, http://dx.doi.org/10.1016/j.aim.2015.06.007
    Journal articles | 2014
    Professor Jie Du
    Du J; Gu H, 2014, 'A realisation of the quantum supergroup U(glm', Journal of Algebra, vol. 404, pp. 60 - 99, http://dx.doi.org/10.1016/j.jalgebra.2013.12.034
    Journal articles | 2014
    Professor Jie Du
    Du J; Gu H; Wang J, 2014, 'Irreducible representations of q-Schur superalgebras at a root of unity', Journal of Pure and Applied Algebra, vol. 218, pp. 2012 - 2059, http://dx.doi.org/10.1016/j.jpaa.2014.03.003
    Journal articles | 2013
    Professor Jie Du
    Deng B; Du J, 2013, 'Identification of simple representations for affine q-Schur algebras', Journal of Algebra, vol. 373, pp. 249 - 275, http://dx.doi.org/10.1016/j.jalgebra.2012.10.013
    Journal articles | 2012
    Professor Jie Du
    Du J; Fu Q; Wang J, 2012, 'Representations of little q-Schur algebras', Pacific Journal of Mathematics, vol. 257, pp. 343 - 378, http://dx.doi.org/10.2140/pjm.2012.257.343
    Journal articles | 2011
    Professor Jie Du
    Du J; Rui H, 2011, 'Quantum Schur superalgebras and Kazhdan-Lusztig combinatorics', Journal of Pure and Applied Algebra, vol. 215, pp. 2715 - 2737, http://dx.doi.org/10.1016/j.jpaa.2011.03.015
    Journal articles | 2010
    Professor Jie Du
    Deng B; Du J, 2010, 'Presenting degenerate Ringel-Hall algebras of cyclic quivers', Journal of Pure and Applied Algebra, vol. 214, pp. 1787 - 1799, http://dx.doi.org/10.1016/j.jpaa.2009.12.021
    Journal articles | 2010
    Professor Jie Du
    Du J; Deng B, 2010, 'Tight monomials and the monomial basis property', Journal of Algebra, vol. 324, pp. 3355 - 3377, http://dx.doi.org/10.1016/j.jalgebra.2010.09.022
    Journal articles | 2010
    Professor Jie Du
    Du J; Fu Q, 2010, 'A modified BLM approach to quantum affine gln', Mathematische Zeitschrift, vol. 266, pp. 747 - 781, http://dx.doi.org/10.1007/s00209-009-0596-6
    Journal articles | 2009
    Professor Jie Du
    Du J; Fu Q, 2009, 'Quantum g iota(infinity) infinite q-Schur algebras and their representations', Journal of Algebra, vol. 322, pp. 1516 - 1547, http://dx.doi.org/10.1016/j.jalgebra.2009.05.035
    Journal articles | 2009
    Professor Jie Du
    Du J; Fu Q, 2009, 'Quantum gl∞, infinite q-Schur algebras and their representations', Journal of Algebra, vol. 322, pp. 1516 - 1547, http://dx.doi.org/10.1016/j.jalgebra.2009.05.035
    Journal articles | 2009
    Professor Jie Du
    Du J; Shu B, 2009, 'Representations of finite Lie algebras', Journal of Algebra, vol. 321, pp. 3197 - 3225, http://dx.doi.org/10.1016/j.jalgebra.2008.06.016
    Journal articles | 2007
    Professor Jie Du
    Deng B; Du J, 2007, 'Folding derived categories with Frobenius functors', Journal of Pure and Applied Algebra, vol. 208, pp. 1023 - 1050, http://dx.doi.org/10.1016/j.jpaa.2006.05.001
    Journal articles | 2007
    Professor Jie Du
    Deng B; Du J; Zhang G, 2007, 'Linear quivers, generic extensions and Kashiwara operators', Indagationes Mathematicae - New Series, vol. 18, pp. 3 - 21, http://dx.doi.org/10.1016/S0019-3577(07)80003-6
    Journal articles | 2007
    Professor Jie Du
    Deng B; Du J; Xiao J, 2007, 'Generic extensions and canonical bases for cyslic quivers', Canadian Journal of Mathematics - Journal Canadien de Mathematiques, vol. 59, pp. 1260 - 1283, http://dx.doi.org/10.4153/CJM-2007-054-7
    Journal articles | 2006
    Professor Jie Du
    Deng B; Du J, 2006, 'Frobenius morphisms and representations of algebras', Transactions of the American Mathematical Society, vol. 358, pp. 3591 - 3622, http://dx.doi.org/10.1090/S0002-9947-06-03812-8
    Journal articles | 2006
    Professor Jie Du
    Deng B; Du J, 2006, 'Algebras, representations and their derived categories over finite fields', Contemporary Mathematics, vol. 413, pp. 25 - 41, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000241190800002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a
    Journal articles | 2005
    Professor Jie Du
    Deng B; Du J, 2005, 'Monomial bases for quantum affine', Advances in Mathematics, vol. 191, pp. 276 - 304, http://dx.doi.org/10.1016/j.aim.2004.03.008
    Journal articles | 2005
    Professor Jie Du
    Deng B; Du J, 2005, 'Bases of quantized enveloping algebras', Pacific Journal of Mathematics, vol. 220, pp. 33 - 48, http://dx.doi.org/10.2140/pjm.2005.220.33
    Journal articles | 2005
    Professor Jie Du
    Du J; Fu Q; Wang J, 2005, 'Infinitesimal quantum and little q-Schur algebras', Journal of Algebra, vol. 287, pp. 199 - 233, http://dx.doi.org/10.1016/j.jalgebra.2005.01.040
    Journal articles | 2005
    Professor Jie Du
    Du J, 2005, 'Robinson-Schensted algorithm and Vogan equivalence', Journal of Combinatorial Theory Series A, vol. 112, pp. 165 - 172, http://dx.doi.org/10.1016/j.jcta.2005.01.008
    Journal articles | 2004
    Professor Jie Du
    Du J; Lin Z, 2004, 'Stratifying algebras with near-matrix algebras', Journal of Pure and Applied Algebra, vol. 188, pp. 59 - 72, http://dx.doi.org/10.1016/j.jpaa.2003.10.016
    Journal articles | 2003
    Professor Jie Du
    Du J, 2003, 'Finite-dimensional algebras and standard systems', Algebras and Representation Theory, vol. 6, pp. 461 - 474, http://dx.doi.org/10.1023/B:ALGE.0000006491.28617.d8
    Journal articles | 2003
    Professor Jie Du
    Du J; Parshall B, 2003, 'Monomial bases for q-Schur algebras', Transactions of the American Mathematical Society, vol. 355, pp. 1593 - 1620, http://dx.doi.org/10.1090/S0002-9947-02-03188-4
    Journal articles | 2002
    Professor Jie Du
    Du J; Parshall B, 2002, 'Linear quivers and the geometric setting of quantum GLn', Indagationes Mathematicae - New Series, vol. 13, pp. 459 - 481, http://dx.doi.org/10.1016/S0019-3577(02)80026-X
    Journal articles | 2001
    Professor Jie Du
    Du J; Rui H, 2001, 'Specht modules for ariki-koike algebras', Communications in Algebra, vol. 29, pp. 4701 - 4719, http://dx.doi.org/10.1081/AGB-100106782
    Journal articles | 2000
    Professor Jie Du
    Du J; Scott LM, 2000, 'The q-Schur2 algebras', Transactions of the American Mathematical Society, vol. 352, pp. 4325 - 4353
    Journal articles | 2000
    Professor Jie Du
    Du J; Rui H, 2000, 'Ariki-Koike algebras with semisimple bottoms', Mathematische Zeitschrift, vol. 234, pp. 807 - 830, http://dx.doi.org/10.1007/s002090050009
    Journal articles | 1999
    Professor Jie Du
    Du J; Rui H, 1999, 'Borel type subalgebras of the q-Schur m algebra', Journal of Algebra, vol. 213, pp. 567 - 595, http://dx.doi.org/10.1006/jabr.1998.7676
    Journal articles | 1999
    Professor Jie Du
    Du J, 1999, 'A new proof for the canonical bases of type A', Algebra Colloquium, vol. 6, pp. 377 - 383
    Journal articles | 1998
    Professor Jie Du
    Du J; Parshall B; Scott LM, 1998, 'Quantum Weyl reciprocity and tilting modules', Communications in Mathematical Physics, vol. 195, pp. 321 - 352, http://dx.doi.org/10.1007/s002200050392
    Journal articles | 1998
    Professor Jie Du
    Du J; Rui H, 1998, 'Based algebras and standard bases for Quasi-Hereditary algebras', Transactions of the American Mathematical Society, vol. 350, pp. 3207 - 3235, http://dx.doi.org/10.1090/S0002-9947-98-02305-8
    Journal articles | 1998
    Professor Jie Du
    Du J; Parshall B; Scott LM, 1998, 'Stratifying endomorphism algebras associated to Hecke algebras', Journal of Algebra, vol. 203, pp. 169 - 210, http://dx.doi.org/10.1006/jabr.1997.7325
    Journal articles | 1998
    Professor Jie Du
    Du J; Parshall B; Scott LM, 1998, 'Cells and q-Schur algebras', Transformation Groups, vol. 3, pp. 33 - 49, http://dx.doi.org/10.1007/BF01237838
    Journal articles | 1997
    Professor Jie Du
    Dipper R; Du J, 1997, 'Harish-Chandra vertices and Steinberg`s tensor product theorems for finite general linear groups', Proceedings of the London Mathematical Society, 3rd Series, vol. 75, pp. 559 - 599, http://dx.doi.org/10.1112/S0024611597000439
    Journal articles | 1996
    Professor Jie Du
    Du J, 1996, 'Cells in certain sets of matrices', Tohoku Mathematical Journal, vol. 48, pp. 417 - 427, http://dx.doi.org/10.2748/tmj/1178225340
    Journal articles | 1996
    Professor Jie Du
    Du J, 1996, 'Global IC bases for quantum linear groups', Journal of Pure and Applied Algebra, vol. 114, pp. 25 - 37, http://dx.doi.org/10.1016/S0022-4049(96)00045-X
    Journal articles | 1995
    Professor Jie Du
    Du J, 1995, 'Q-Schur algebras, asymptotic forms and quantum SLn', Journal of Algebra, vol. 177, pp. 385 - 408, http://dx.doi.org/10.1006/jabr.1995.1304
    Journal articles | 1995
    Professor Jie Du
    Du J, 1995, 'Canonical bases for irreducible representations of quantum GLn, II', Journal of the London Mathematical Society - Second Series, vol. 51, pp. 461 - 470, http://dx.doi.org/10.1112/jlms/51.3.461
    Journal articles | 1995
    Professor Jie Du
    Du J, 1995, 'A note on quantized Weyl reciprocity at roots of unity', Algebra Colloquium, vol. 2, pp. 363 - 372
    Journal articles | 1994
    Professor Jie Du
    Du J; Scott L, 1994, 'Lusztig conjectures, old and new, I', Journal fur die Reine und Angewandte Mathematik, vol. 1994, pp. 141 - 182, http://dx.doi.org/10.1515/crll.1994.455.141
    Journal articles | 1991
    Professor Jie Du
    Du J; Parshall B; Wang J-P, 1991, 'Two-Parameter Quantum Linear Groups and the Hyperbolic Invariance of q -Schur Algebras', Journal of the London Mathematical Society, vol. s2-44, pp. 420 - 436, http://dx.doi.org/10.1112/jlms/s2-44.3.420
  • Conference Papers | 2016
    Professor Jie Du
    Du J, 2016, 'Structure and representations of the quantum loop algebra', in Proceedings of The 7th International Congress of Chinese Mathematicians, Beijing, China, presented at 7th International Congress of Chinese Mathematicians, Beijing, China, 06 April 2016 - 11 August 2016
    Conference Papers | 2012
    Professor Jie Du
    Du J, 2012, 'Structure and representations of affine q-Schur algebras', in Proceedings of Symposia in Pure Mathematics, Vol 86, American Mathematical Society, University of Virginia, pp. 137 - 158, presented at Southeastern Lie Theory Workshop: Finite and Algebraic Groups, University of Virginia, 01 June 2011 - 04 June 2011
    Conference Papers | 2010
    Professor Jie Du
    Deng B; Du J; Mah A, 2010, 'Generic extensions and composition monoids of cyclic quivers', in Chari V; Greenstein J; Misra KC; Raghavan KN; Viswanath S (eds.), Recent Developments in Algebraic and Combinatorial Aspects of Representation Theory, American Mathematical Society, Bangalore, India, pp. 99 - 114, presented at International Congress of Mathematicians Satellite Conference Algebraic and Combinatorial Approaches to Represenation Theory, Bangalore, India, 12 August 2010 - 16 August 2010
    Conference Papers | 2007
    Professor Jie Du
    Du J; Rui H, 2007, 'Multi-parameter cells of finite Coxeter groups', in International Conference on Complex Geometry and Related Fields, International Conference on Complex Geometry and Related Fields, Shanghai, presented at International Conference on Complex Geometry and Related Fields, Shanghai, 01 July 2004
    Conference Papers | 2004
    Professor Jie Du
    Du J, 2004, 'Finite Dimensional Algebras, Quantum Groups and Finite Groups of Lie Type', in Fields Institute Communications, Fields Institute Communications, Toronto, USA, presented at Fields Institute Communications, Toronto, USA, 01 August 2002
    Conference Papers | 2000
    Professor Jie Du
    Du J; Scott LM, 2000, 'Stratifying q-Schur algebras', in international conference on representation theory, international conference on representation theory, Shanghai, China, presented at international conference on representation theory, Shanghai, China, 29 June 1998 - 03 July 1998
    Conference Papers | 1998
    Professor Jie Du
    Du J, 1998, 'Generalised q-Schur algebras and the ways to approach them', in Collins MJ; Parshall BJ; Scott LL (eds.), A symposium held at the University of Virginia, WALTER DE GRUYTER GMBH, Virginia, pp. 189 - 210, presented at a symposium held at the University of Virginia, Virginia, 08 May 1998 - 15 May 1998, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000175524900007&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a

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