# Slaven Kožić (University of Sydney)

## Quasi-particle bases of standard $$\widehat{\mathfrak{sl}}_{2}$$-modules

The aim of this talk is to present some connections between the representation theory of the affine Lie algebra $$\widehat{\mathfrak{sl}}_{2}$$ and the Rogers-Ramanujan-type identities. I will define quasi-particles in the principal picture of $$\widehat{\mathfrak{sl}}_{2}$$ and construct quasi-particle monomial bases of standard $$\widehat{\mathfrak{sl}}_{2}$$-modules. Finally, 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.