Twisting functors and Gelfand-Tsetlin modules over semisimple Lie algebras

Futorny，Vyacheslav1,2; Křižka，Libor1

2022

10.1142/S0219199722500316

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS   Impact Factor & Quartile

0219-1997

We associate to an arbitrary positive root α of a complex semisimple finite-dimensional Lie algebra a twisting endofunctor Tα of the category of -modules. We apply this functor to generalized Verma modules in the category () and construct a family of α-Gelfand-Tsetlin modules with finite Fα-multiplicities, where Fα is a commutative ℂ-subalgebra of the universal enveloping algebra of generated by a Cartan subalgebra of and by the Casimir element of the (2)-subalgebra corresponding to the root α. This covers classical results of Andersen and Stroppel when α is a simple root and previous results of the authors in the case when is a complex simple Lie algebra and α is the maximal root of . The significance of constructed modules is that they are Gelfand-Tsetlin modules with respect to any commutative ℂ-subalgebra of the universal enveloping algebra of containing Fα. Using the Beilinson-Bernstein correspondence we give a geometric realization of these modules together with their explicit description. We also identify a tensor subcategory of the category of α-Gelfand-Tsetlin modules which contains constructed modules as well as the category ().

Gelfand-Tsetlin module generalized Verma module Twisting functor Weyl algebra-module

SCI

English

Corresponding

WOS:000849384000001

MATHEMATICS

2-s2.0-85137232008

Scopus

1.Instituto de Matemática e Estatística,Universidade de São Paulo,São Paulo,Brazil
2.International Center for Mathematics,SUSTech,Shenzhen,China

Futorny，Vyacheslav,Křižka，Libor. Twisting functors and Gelfand-Tsetlin modules over semisimple Lie algebras[J]. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS,2022.

Futorny，Vyacheslav,&Křižka，Libor.(2022).Twisting functors and Gelfand-Tsetlin modules over semisimple Lie algebras.COMMUNICATIONS IN CONTEMPORARY MATHEMATICS.

Futorny，Vyacheslav,et al."Twisting functors and Gelfand-Tsetlin modules over semisimple Lie algebras".COMMUNICATIONS IN CONTEMPORARY MATHEMATICS (2022).