The regular representation of U_v(\mathfrakgl_m|n)

2019/05/06 by Du, Jie, Zhou, Zhongguo · 1 citation
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1905.01828

Abstract

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

Cited by

• Three approaches to the Howe duality between quantum general linear supergroups

Related

• A realisation of the quantum linear superalgebra
• Polynomial super representations of the hyperalgebra of \mathfrakgl_m|n at roots of unity
• On the quantum superalgebra U_q(gl(m,n)) and its representations at roots of 1
• Quantum queer supergroups via v-differential operators
• Canonical bases for the quantum linear supergroups