Gelfand-Tsetlin Crystals of Kostant-Kumar modules
Mrigendra Singh Kushwaha
TL;DR
This paper constructs Gelfand-Tsetlin crystal bases for Kostant-Kumar modules of type A Lie algebras and introduces a polytopal model using BiKogan faces, enhancing combinatorial understanding.
Contribution
It provides explicit Gelfand-Tsetlin crystals and a polytopal model for Kostant-Kumar modules in type A, linking crystal bases with geometric combinatorics.
Findings
Gelfand-Tsetlin crystals are constructed for Kostant-Kumar modules.
A polytopal model using BiKogan faces is established.
The work connects crystal bases with geometric combinatorics in type A.
Abstract
We give Gelfand-Tsetlin crystals for the Kostant-Kumar modules for the finite simple Lie algebra of type A. Kostant-Kumar modules are cyclic submodules of the tensor product of two irreducible highest weight modules of a symmetrizable Kac-Moody Lie algebras. In this case (type A), we also provide a polytopal model for Kostant-Kumar modules in terms of BiKogan faces.
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Taxonomy
TopicsAdvanced Algebra and Logic · Algebraic structures and combinatorial models · graph theory and CDMA systems