This talk will discuss some connections between the representation theory of the affine Lie algebra slˆ2sl^2
and the Rogers-Ramanujan-type identities.
After providing some introductory definitions and results, I will introduce quasi-particles in the principal picture of slˆ2sl^2 and construct quasi-particle monomial bases
of standard slˆ2sl^2-modules. I will show that their principally specialized characters are given as products of sum sides of the corresponding Rogers-Ramanujan-type identities with the character of the Fock space for the principal Heisenberg subalgebra.
This is a joint work with Mirko Primc.