Gelfand-Tsetlin modules over gl(n) with arbitrary characters

JOURNAL OF ALGEBRA

卷:502

Article

Ramirez, L. E.¹  Zadunaisky, P.² 

[1] Univ Fed ABC, Santo Andre, SP, Brazil

[2] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo, SP, Brazil

关键词: Gelfand-Tsetlin modules;    Gelfand-Tsetlin bases;    Tableaux realization;   

DOI  :  10.1016/j.jalgebra.2018.01.034

来源: Elsevier

【 摘 要 】

A Gelfand-Tsetlin tableau T(v) induces a character X-v of the Gelfand-Tsetlin subalgebra Gamma of U = U(gl(n, C)). By a theorem due to Ovsienko, for each tableau T(v) there exists a finite number of nonisomorphic irreducible Gelfand-Tsetlin modules with X-v in its support, though explicit examples of such modules are only known for special families of characters. In this article we build a family of Gelfand-Tsetlin modules parametrized by characters, such that each character appears in its corresponding module. We also find the support of these modules, with multiplicities. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free