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<p>We give Gelfand–Tsetlin crystals for the Kostant–Kumar modules for the finite simple Lie algebra of type <i>A</i>. Kostant–Kumar modules are cyclic submodules of the tensor product of two irreducible highest weight modules of a symmetrizable Kac–Moody Lie algebra. In this case (type <i>A</i>), we also provide a polytopal model for Kostant–Kumar modules in terms of <i>BiKogan faces</i>.</p>

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Gelfand–Tsetlin crystals of Kostant–Kumar modules

  • 期刊论文

  • 发表日期：

    2025年7月25日

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  • Mrigendra Singh Kushwaha

摘要

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 algebra. In this case (type A), we also provide a polytopal model for Kostant–Kumar modules in terms of BiKogan faces.