- Date: 2024-11-22 (금요일) 10:00 ~ 11:30
2024-11-29 (금요일) 10:00 ~ 11:30
- Place: Zoom (ID: 819 6329 7436 PW: 856972)
- Speaker: 서의린 (Seoul National University)
- Title: W-algebras and Quantum affine algebras
- Abstract:
Lecture 1: Basics of W-algebras (2024-11-22 10:00 ~ 11:30)
A finite W-algebra of Lie algebra is a quantum Hamiltonian reduction of the universal enveloping algebra. In 1950’s, Kostant proved that principal finite W-algebra is isomorphic to the center of the enveloping algebra. Also, the projection of the W-algebra onto the enveloping algebra of the Cartan subalgebra called Miura map is injective. In this lecture, I will explain these properties with examples and affine analogues of these properties : free field realization and Miura transformation.
Lecture 2: From W-algebras to Quantum affine algebras (2024-11-29 10:00 ~ 11:30)
In between the theory of W-algebras and Quantum affine algebras, the object called deformed W-algebras take place. Especially, the q-character of Quantum affine algebras can be interpreted using the notion of deformed W-algebras. In order to understand the complicated construction of deformed W-algebras, one needs to understand free field realization of affine W-algebras via screening operators. In this talk, I will explain via screening operators and how we generalize this construction to derive deformed W-algebras.