Baker-Akhiezer function as iterated residue and Selberg-type integral

TL;DR

This paper introduces new integral formulas for the Baker-Akhiezer function associated with the $A_n$ root system, using iterated residues and Selberg-type integrals, including a generalization to the deformed $A_{n,1}$ case.

Contribution

It provides explicit integral representations of the Baker-Akhiezer function in rational, trigonometric, and deformed cases, expanding the class of known Selberg-type integral evaluations.

Findings

Integral formula as an iterated residue for the Baker-Akhiezer function.

Selberg-type integral formula for the Baker-Akhiezer function.

Generalization to the deformed $A_{n,1}$-case.

Abstract

A simple integral formula as an iterated residue is presented for the Baker-Akhiezer function related to $A_n$ type root system both in the rational and trigonometric cases. We present also a formula for the Baker-Akhiezer function as a Selberg-type integral and generalise it to the deformed $A_{n,1}$-case. These formulas can be interpreted as new cases of explicit evaluation of Selberg-type integrals.