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- W2900820791 abstract "We introduce the notion of essential support of a simple Gelfand-Tsetlin $mathfrak{gl}_n$-module as an important tool towards understanding the character formula of such module. This support detects the weights in the module 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 a socle of a universal tableaux module and hence obtain a description of the essential supports of all simple Verma modules. As a consequence, we prove the Strong Futorny-Ovsienko Conjecture on the sharpness of the upper bounds of the Gelfand-Tsetlin multiplicities. In addition we give a very explicit description of the support and essential support of the simple singular Verma module $M(-rho)$" @default.
- W2900820791 created "2018-11-29" @default.
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- W2900820791 date "2018-11-19" @default.
- W2900820791 modified "2023-10-12" @default.
- W2900820791 title "Bounds of Gelfand-Tsetlin multiplicities and tableaux realizations of Verma modules" @default.
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