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arXiv · 2004.11069

Finite dimensional simple modules of $(q, \mathbf{Q})$-current algebras

Ryosuke Kodera·Kentaro Wada
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Abstract

The $(q, \mathbf{Q})$-current algebra associated with the general linear Lie algebra was introduced by the second author in the study of representation theory of cyclotomic $q$-Schur algebras. In this paper, we study the $(q, \mathbf{Q})$-current algebra $U_q(\mathfrak{sl}_n^{\langle \mathbf{Q} \rangle}[x])$ associated with the special linear Lie algebra $\mathfrak{sl}_n$. In particular, we classify finite dimensional simple $U_q(\mathfrak{sl}_n^{\langle \mathbf{Q} \rangle}[x])$-modules.

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BibTeXRIS

Ryosuke Kodera, Kentaro Wada. 2020-04-23. Finite dimensional simple modules of $(q, \mathbf{Q})$-current algebras. https://arxiv.org/abs/2004.11069

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