A trial to find an elliptic quantum algebra for $sl_2$ using the Heisenberg and Clifford algebra

TL;DR

This paper explores a two-parameter deformation of the quantum algebra $U(sl_2)$ using Heisenberg and Clifford algebra realizations, revealing connections with theta functions.

Contribution

It introduces a novel realization of a deformed $U(sl_2)$ algebra via Heisenberg and Clifford algebras, linking it to theta functions.

Findings

Deformation of $U(sl_2)$ with parameters p and q

Connection between algebra relations and theta functions

New realization approach for quantum algebra

Abstract

A Heisenberg-Clifford realization of a deformed $U(sl_{2})$ by two parameters $p$ and $q$ is discussed. The commutation relations for this deformed algebra have interesting connection with the theta functions.