University of Sydney Algebra Seminar

Slaven Kožić (University of Sydney)

Friday 7 October, 12-1pm, Place: Carslaw 375

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.