Quantization of the shift of argument subalgebras in type A

Author(s)

Futorny, Vyacheslav ^[1] ; Molev, Alexander ^[2]

Affiliation

^[1] Univ Sao Paulo, Dept Math, BR-05315970 Sao Paulo, SP - Brazil

^[2] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006 - Australia

• Document type: Journal article
• Source: ADVANCES IN MATHEMATICS; v. 285, p. 1358-1375, NOV 5 2015.
• Web of Science Citations: 2

Abstract

Given a simple Lie algebra g and an element mu is an element of g{*}, the corresponding shift of argument subalgebra of S(g) is Poisson commutative. In the case where mu is regular, this subalgebra is known to admit a quantization, that is, it can be lifted to a commutative subalgebra of U(g). We show that if g is of type A, then this property extends to arbitrary mu thus proving a conjecture of Feigin, Frenkel and Toledano Laredo. The proof relies on an explicit construction of generators of the center of the affine vertex algebra at the critical level. (C) 2015 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 10/50347-9 - Algebras, representations e applications
• Grantee: Ivan Chestakov
• Support Opportunities: Research Projects - Thematic Grants