Speaker: Shashank Kannade
Affiliation: University of Denver
Title: Combinatorics of affine Lie algebra characters
Date and Time: November 24, 2023, 11:00:00 Hours
Venue: AG-77
Asbtract: About four decades ago, Lepowsky and Wilson gave the first fully representation-theoretic proof of the Rogers--Ramanujan identities using the affine Lie algebra $\widehat{\mathfrak{sl}}_2$. In 1999, Andrews, Schilling and Warnaar found and proved some (but not all) infinite families of identities related to $\widehat{\mathfrak{sl}}_3$. In a recent joint work with Russell, we gave conjectures that encompass all the remaining identities for $\widehat{\mathfrak{sl}}_3$, and proved our conjectures at low levels. Our (univariate) conjectures have been recently proved by Warnaar. However, our bivariate conjectures, related to $3$-rowed cylindric partitions, remain open. In general, cylindric partitions control the combinatorics of minimal series principal $W_r(p,p')$ algebras of type $\mathfrak{sl}_r$. I will explain these developments.
Affiliation: University of Denver
Title: Combinatorics of affine Lie algebra characters
Date and Time: November 24, 2023, 11:00:00 Hours
Venue: AG-77
Asbtract: About four decades ago, Lepowsky and Wilson gave the first fully representation-theoretic proof of the Rogers--Ramanujan identities using the affine Lie algebra $\widehat{\mathfrak{sl}}_2$. In 1999, Andrews, Schilling and Warnaar found and proved some (but not all) infinite families of identities related to $\widehat{\mathfrak{sl}}_3$. In a recent joint work with Russell, we gave conjectures that encompass all the remaining identities for $\widehat{\mathfrak{sl}}_3$, and proved our conjectures at low levels. Our (univariate) conjectures have been recently proved by Warnaar. However, our bivariate conjectures, related to $3$-rowed cylindric partitions, remain open. In general, cylindric partitions control the combinatorics of minimal series principal $W_r(p,p')$ algebras of type $\mathfrak{sl}_r$. I will explain these developments.