Quantum Supergroup $U_{r,s}(osp(1,2))$, Scasimir Operators, and Dickson polynomials

TL;DR

This paper investigates the center of a two-parameter quantum supergroup using Dickson polynomials, revealing that the Scasimir operator is characterized by a q-deformed Chebyshev polynomial, thus generalizing previous results.

Contribution

It introduces a novel connection between the Scasimir operator and q-deformed Chebyshev polynomials within the context of quantum supergroups.

Findings

The center of $U_{r,s}(osp(1,2))$ is characterized using Dickson polynomials.

The Scasimir operator is explicitly determined by a q-deformed Chebyshev polynomial.

The work generalizes earlier results by Arnaudon and Bauer.

Abstract

We study the center of the two-parameter quantum supergroup $U_{r,s}(osp(1,2))$ using the Dickson polynomial. We show that the Scasimir operator is completely determined by the $q$-deformed Chebychev polynomial, generalizing an earlier work of Arnaudon and Bauer.