# 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.

## Key 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.