The square integrable representations on generalized Weyl-Heisenberg groups

TL;DR

This paper studies square integrable representations of generalized Weyl-Heisenberg groups, analyzing their quasi-regular representations, deriving admissible vectors, and providing examples to illustrate the theoretical findings.

Contribution

It introduces explicit forms for admissible vectors in the square integrable representations of generalized Weyl-Heisenberg groups, expanding understanding of their structure.

Findings

Derived concrete forms for admissible vectors

Analyzed the quasi-regular representation structure

Provided examples supporting theoretical results

Abstract

This paper presents the square integrable representations of generalized Weyl-Heisenberg group. We investigate the quasi regular representation of generalized Weyl-Heisenberg group. Moreover, we obtain a concrete from for admissible vector of this representation. Finally, we provide some examples to support our technical considerations.