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Bounds of Gelfand-Tsetlin multiplicities and tableaux realizations of Verma modules
(Academic Press Inc Elsevier Science, 2020-08)
We introduce the notion of essential support of a simple Gelfand-Tsetlin gln-module as an attempt to understand the character formula of such module. This support detects the weights having maximal possible Gelfand-Tsetlin ...
The Gelfand-Kirillov conjecture and Gelfand-Tsetlin modules for finite W-algebras
(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2010)
We address two problems with the structure and representation theory of finite W-algebras associated with general linear Lie algebras. Finite W-algebras can be defined using either Kostant`s Whittaker modules or a quantum ...
A geometric approach to 1-singular gelfand-tsetlin gln -modules
(Universidade Federal de Minas GeraisBrasilICX - DEPARTAMENTO DE MATEMÁTICAUFMG, 2018-02)
Este artigo é dedicado a uma nova construção elementar de módulos de Gelfand – Tsetlin de 1 singular usando geometria complexa. Introduzimos um anel universal Dv junto com o espaço vetorial S = S (Dv) com base Bv = B (Dv) ...
A new way to construct 1-singular Gelfand-Tsetlin modules
(Lugansk Taras Shevchenko National University, 2017-04)
We present a simplified way to construct the Gelfand-Tsetlin modules over gl(n,C) related to a 1-singular GT-tableau defined by Futorny, Grantcharov and Ramirez. We begin by reframing the classical construction of generic ...