Evaluation of the $BC_n$ elliptic Selberg integral via the fundamental invariants

TL;DR

This paper provides an alternative proof for the elliptic Selberg integral of type BC_n using fundamental BC_n-invariants, offering new insights into its evaluation formula.

Contribution

It introduces a novel proof method for the elliptic Selberg integral of type BC_n based on fundamental invariants, enhancing understanding of its structure.

Findings

Alternative proof of the elliptic Selberg integral evaluation

Application of fundamental BC_n-invariants in integral evaluation

Deeper understanding of elliptic integral structures

Abstract

We give an alternative proof of the evaluation formula for the elliptic Selberg integral of type $BC_n$ as an application of the fundamental $BC_n$-invariants.