Quantum sphere S^4 as a non-Levi conjugacy class

TL;DR

This paper develops a quantum deformation of the four-dimensional complex sphere viewed as a conjugacy class with a non-Levi isotropy subgroup, using operator realization on a highest weight module.

Contribution

It introduces a U_h(sp(4))-equivariant quantization of S^4 as a non-Levi conjugacy class, expanding the understanding of quantum homogeneous spaces.

Findings

Constructed a quantum polynomial algebra C_h[S^4]

Realized the quantization via operators on a highest weight module

Provided a new example of non-Levi conjugacy class quantization

Abstract

We construct a U_h(sp(4))-equivariant quantization of the four-dimensional complex sphere S^4 regarded as a conjugacy class, Sp(4)/Sp(2)x Sp(2), of a simple complex group with non-Levi isotropy subgroup, through an operator realization of the quantum polynomial algebra C_h[S^4] on a highest weight module of U_h(sp(4)).