Orthogonal polynomials and Lie superalgebras

TL;DR

This paper explores the connection between orthogonal polynomials and Lie superalgebras, specifically OSP(1|2n), and discusses challenges in expressing Dyson's constant for these superalgebras.

Contribution

It introduces a new set of orthogonal polynomials derived from the Lie superalgebra OSP(1|2n) for the orthogonal Lie algebra O(2n+1).

Findings

A new set of orthogonal polynomials associated with OSP(1|2n)

Discussion of difficulties in expressing Dyson's constant for Lie superalgebras

Insights into the structure of orthogonal polynomials related to superalgebras

Abstract

For the orthogonal Lie algebra O(2n+1), in addition to the conventional set of orthogonal polynomials, another set is produced with the help of the Lie superalgebra OSP(1|2n). Difficulties related with expression of Dyson's constant for the Lie superalgebras are discussed.