The regular representation of $U_v({\mathfrak{gl}}_{m|n})$

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.

15 pages

References in corpus (1)

• Polynomial super representations of the hyperalgebra of ${\mathfrak{gl}}_{m|n}$ at roots of unity