Hilbert series and Berezin-Gelfand duality

TL;DR

This paper explores the appearance of Jacobi and Hahn polynomials in the Hilbert series of certain homogeneous spaces, illustrating their mathematical relationships.

Contribution

It provides an example linking special orthogonal polynomials to the Hilbert series of homogeneous spaces, highlighting a novel connection.

Findings

Jacobi polynomials appear in Hilbert series

Hahn polynomials as discrete counterparts in the series

Illustration of polynomial roles in geometric contexts

Abstract

We give an example showing how Jacobi polynomials and their discrete counterparts (Hahn polynomials) appear in the Hilbert series of some homogeneous spaces.