Quantization of the shift of argument subalgebras in type A

Autor(es)

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

Afiliação do(s) autor(es)

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

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

• Tipo de documento: Artigo Científico
• Fonte: ADVANCES IN MATHEMATICS; v. 285, p. 1358-1375, NOV 5 2015.
• Citações Web of Science: 2

Resumo

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)

• Processo FAPESP: 10/50347-9 - Álgebras, representações e aplicações
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Temático