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The regular representation of $U_v(\mathfrak{gl}_{m|n})$ (1905.01828v1)
Published 6 May 2019 in math.QA, math.RA, and math.RT
Abstract: Using quantum differential operators, we construct a super representation of $U_v(\mathfrak{gl}{m|n})$ on a certain polynomial superalgebra. We then extend the representation to its formal power series algebra which contains a $U_v(\mathfrak{gl}{m|n})$-submodule isomorphic to the regular representation of $U_v(\mathfrak{gl}{m|n})$. In this way, we obtain a presentation of $U_v(\mathfrak{gl}{m|n})$ by a basis together with explicit multiplication formulas of the basis elements by generators.