Elliptic Hypergeometric Functions

TL;DR

This paper provides an elementary introduction to elliptic hypergeometric functions, highlighting their historical origin in solvable lattice models and presenting a new proof relating to elliptic solid-on-solid models.

Contribution

It offers a simplified explanation of elliptic hypergeometric functions and introduces a novel proof connecting these functions to fused Boltzmann weights in lattice models.

Findings

Elliptic hypergeometric functions are linked to solvable lattice models.

A new proof shows fused Boltzmann weights can be expressed as elliptic hypergeometric sums.

The lecture notes emphasize motivation and main ideas over comprehensive survey.

Abstract

In these lecture notes I give an elementary introduction to elliptic hypergeometric functions. I focus on motivating the main ideas and constructions, rather than giving a comprehensive survey. The lectures include a brief explanation of the historical origin of elliptic hypergeometric functions in the context of solvable lattice models. In particular, I give a new proof of the fact that fused Boltzmann weights for the elliptic solid-on-solid model can be expressed as elliptic hypergeometric sums.