Mini-workshop on deformed W-algebras and q-characters II
- Date: 2022-06-16 (Thu)
- Place: 129-406 (SNU)
9:00 ~ 10:00
Speaker: 서의린 (SNU)
Title: Constructions of W-algebras
Abstract: In this talk, I will briefly review two of most well-known constructions of classical and quantum W-algebras. The first part will be about Drinfeld-Sokolov reduction and the second part will be about screening operators. I will also show how these two constructions are related to each other in both classical and quantum cases.
10:30 ~ 12:00
Speaker: 장일승 (QSMS, SNU)
Title: Introduction to q-characters
Abstract: Let U' be the quantum affine algebra corresponding to an affine Lie algebra (of untwisted type). In [arXiv:math/9810055], Frenkel and Reshetikhin provided a refined notion of the ordinary character in the category of finite-dimensional U'-modules, so-called q-character, motivated by their theory of deformed W-algebras. In this talk, I will briefly introduce the q-character and discuss it, focusing mainly on type A with rank 1 or 2.
14:00 ~ 15:30
Speaker: 김영훈 (QSMS, SNU)
Title: Computation of q-characters of finite dimensional modules of quantum affine algebras
Abstract: In 1998, Frenkel and Reshetikhin introduced an injective ring homomorphism, called the q-character, from the Grothendieck ring of finite-dimensional modules of a quantum affine algebra to a ring of Laurent polynomials. In this talk, we first study some basic properties of the q-character. Then, we explicitly compute q-characters for some example modules.
16:00 ~ 17:00
Speaker: 이신명 (SNU)
Title: Deformed W-algebras and q-characters
Abstract: In this talk, we investigate relations between deformed W-algebras and finite-dimensional representations of quantum affine algebras. We first define various deformed W-algebras by means of screening operators. Among them, we focus on q-deformed W-algebras, whose free field realization can be identified with the q-character map. Finally, we give a brief survey on more recent results on both sides.