Representations of $\pmb {U_q(\mathfrak {gl}_2)}$ at roots of unity

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2025年8月27日

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Snehashis Mukherjee

摘要

In this article, we embark on a comprehensive exploration of the irreducible representations of the quantum enveloping algebra $U_q(\mathfrak {gl}_2)$ $U_{q} ({gl}_{2})$ at the roots of unity. Within this context, this algebra transform into polynomial identity algebras, imposing constraints on the dimensions of their simple modules through the notion of PI degree. Leveraging the PI degree of the algebra, we present a thorough classification of simple $U_q(\mathfrak {gl}_2)$ $U_{q} ({gl}_{2})$ -modules.

Representations of \(\pmb {U_q(\mathfrak {gl}_2)}\) at roots of unity

摘要