On product type actions of G_q

TL;DR

This paper investigates a specific class of quantum group actions, showing they originate from simpler torus actions, and classifies these actions for SU_q(2), also analyzing related deformations and their intrinsic groups.

Contribution

It proves that faithful product type actions of G_q are induced from minimal actions of its maximal torus, enabling classification of SU_q(2) actions and computation of associated deformation groups.

Findings

Product type actions of G_q are induced from maximal torus actions.

Classification of SU_q(2) product type actions up to conjugacy.

Calculation of the intrinsic group of the deformed quantum group G_{q, Omega}.

Abstract

We will study a faithful product type action of G_q that is the q-deformation of a connected semisimple compact Lie group G, and prove that such an action is induced from a minimal action of the maximal torus T of G_q. This enables us to classify product type actions of SU_q(2) up to conjugacy. We also compute the intrinsic group of G_{q,\Omega}, the 2-cocycle deformation of G_q that is naturally associated with the quantum flag manifold T\backslash G_q.