Bounds of Gelfand-Tsetlin multiplicities and tableaux realizations of Verma modules

JOURNAL OF ALGEBRA

卷:556

Article

Futorny, Vyacheslav¹  Grantcharov, Dimitar²  Ramirez, Luis Enrique³  Zadunaisky, Pablo^4,5 

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

[2] Univ Texas Arlington, Arlington, TX 76019 USA

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

[4] Univ CAECE, Buenos Aires, DF, Argentina

[5] Univ Buenos Aires, Buenos Aires, DF, Argentina

关键词: Gelfand-Tsetlin modules;    Gelfand-Tsetlin bases;    Reflection groups;    Verma modules;   

DOI  :  10.1016/j.jalgebra.2020.02.032

来源: Elsevier

【 摘 要 】

We introduce the notion of essential support of a simple Gelfand-Tsetlin gl(n)-module as an attempt to understand the character formula of such module. This support detects the weights having maximal possible Gelfand-Tsetlin multiplicities. Using combinatorial tools we describe the essential supports of the simple socles of the universal tableaux modules. We also prove that every simple Verma module appears as the socle of a universal tableaux module. As a consequence, we prove the Strong Futorny-Ovsienko Conjecture on the sharpness of the upper bounds of the Gelfand-Tsetlin multiplicities. We also give a very explicit description of the support and essential support of the simple singular Verma module M(-rho). (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free