**Mini-workshop on deformed W-algebras and q-characters I **

Date : 2022-05-31 (Tue)

Place : 27-220 (SNU)

Time table:

- 9:30~11:00

Speaker: 이강산 (SNU)

Title: Introduction to vertex algebras and W-algebras

Abstract: The vertex algebras introduced by R. E. Borcherds are defined by operator-valued formal series with some axioms. In this talk, I will introduce basic properties of vertex algebras and some examples, including affine vertex algebras. Also, I will show how to get W-algebras as Hamiltonian reductions of affine vertex algebras.

- 13:30~15:00

Speaker: 최동준 (SNU)

Title: Classical W-algebra and scalar Lax equation.

Abstract: Classical W-algebra W(sl_n) can be realized by a scalar Lax equation of degree n. By replacing derivation in the Lax operator with the difference operator, we can construct t-deformed W-algebra W_{1,t} (sl_n). In this talk, I will introduce the construction of W_{1,t} (sl_n). If time allows, I will discuss the algebraic structure of W_{1,t} (sl_n)

- 15:30~17:00

Speaker: 송아림 (SNU)

Title: Screening operators for quantum W-algebras

Abstract : Frenkel and Reshetikhin defined q, t-deformed W-algebra in deformed Heisenberg algebra using screening operators $S^-_i$ and $S^+_i$. To understand this algebra, we take a look at quantum W-algebra, which is obtained by specializing q and t. In this talk, we show the realization of quantum W-algebras as subalgebras of Heisenberg algebras, which explains the screening operators $S^-_i$. After that, we would see Feigin Frenkel duality, which explains the other screening operators $S^+_i$.