The regular representation of 𝑈_{𝜐}(𝔤𝔩_{𝔪|𝔫})

Du, Jie; Zhou, Zhongguo

doi:10.1090/proc/14688

The regular representation of $U_{\boldsymbol {\upsilon }}(\mathfrak {gl}_{m|n})$
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by Jie Du and Zhongguo Zhou PDF

Proc. Amer. Math. Soc. 148 (2020), 111-124 Request permission

Abstract:

Using quantum differential operators, we construct a super representation of $U_{\boldsymbol {\upsilon }}(\mathfrak {gl}_{m|n})$ on a certain polynomial superalgebra. We then extend the representation to its formal power series algebra which contains a $U_{\boldsymbol {\upsilon }}(\mathfrak {gl}_{m|n})$-submodule isomorphic to the regular representation of $U_{\boldsymbol {\upsilon }}(\mathfrak {gl}_{m|n})$. In this way, we obtain a presentation of $U_{\boldsymbol {\upsilon }}(\mathfrak {gl}_{m|n})$ by a basis together with explicit multiplication formulas of the basis elements by generators.

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