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arXiv · 2208.05831

Shapovalov Elements For $U_q(\mathfrak{sl}(N+1))

Stefan Catoiu·Ian M. Musson
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Abstract

For a simple Lie algebra, Shapovalov elements give rise to highest weight vectors in Verma modules. The usual construction of these elements uses induction on the length of a certain Weyl group element. If $\mathfrak{g}= \mathfrak{sl}(N+1)$ explicit expressions for Shapovalov elements were given in [Mus22a]. Here we adapt the argument to the quantized enveloping algebra of $\mathfrak{g}$.

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BibTeXRIS

Stefan Catoiu, Ian M. Musson. 2022-08-11. Shapovalov Elements For $U_q(\mathfrak{sl}(N+1)). https://arxiv.org/abs/2208.05831

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