Bounds of Gelfand-Tsetlin multiplicities and tableaux realizations of Verma modules
| Autor: | Futorny, Vyacheslav, Grantcharov, Dimitar, Ramirez, Luis Enrique, Zadunaisky, Pablo |
|---|---|
| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $M(-\rho)$ Comment: 25 pages, some changes made to Introduction in the new version |
| Databáze: | arXiv |
| Externí odkaz: |
|