Mirabolic Howe duality

TL;DR

This paper introduces a new duality concept between mirabolic quantum groups, extending the classical Howe duality to the mirabolic setting, and provides foundational results for this novel mathematical framework.

Contribution

It establishes the first known duality between mirabolic quantum groups, expanding the scope of Howe duality to a new class of quantum groups.

Findings

Defined mirabolic quantum groups and their duality

Proved the duality theorem for the mirabolic case

Lays groundwork for further research in mirabolic quantum algebra

Abstract

We establish a duality between a pair of mirabolic quantum groups, i.e., the mirabolic counterpart of quantum Howe duality.