2018/11/19 by Vyacheslav Futorny, Futorny, Vyacheslav, Dimitar Grantcharov +5
Mathematics · #16G99 #17B10 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1811.07992
openalex publication_date 2018/11/19 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28
We introduce the notion of essential support of a simple Gelfand-Tsetlin\n mathfrakgln-module as an important tool towards understanding the\ncharacter formula of such module. This support detects the weights in the\nmodule having maximal possible Gelfand-Tsetlin multiplicities. Using\ncombinatorial tools we describe the essential supports of the simple socles of\nthe universal tableaux modules. We also prove that every simple Verma module\nappears as a socle of a universal tableaux module and hence obtain a\ndescription of the essential supports of all simple Verma modules. As a\nconsequence, we prove the Strong Futorny-Ovsienko Conjecture on the sharpness\nof the upper bounds of the Gelfand-Tsetlin multiplicities. In addition we give\na very explicit description of the support and essential support of the simple\nsingular Verma module M(-\ρ)\n