Multiparameter quantum function algebra at roots of 1

TL;DR

This paper investigates the representation theory of a multiparameter quantum function algebra at roots of unity, extending existing techniques from the standard quantum case to this more general setting.

Contribution

It introduces new methods for studying multiparameter quantum groups at roots of unity, expanding the theoretical framework beyond the standard quantum case.

Findings

Extended De Concini-Lyubashenko techniques to multiparameter cases

Developed a representation theory framework for multiparameter quantum groups at roots of unity

Provided foundational results for future research in multiparameter quantum algebra

Abstract

We study the theory of representations of a multiparameter deformation of the function algebra of a simple algebraic group (as defined by Reshetikhin) when the quantum parameter is a root of unity. We extend the technics of De Concini-Lyubashenko in the standard quantum case.