Derivation of the Supersymmetric Harish--Chandra Integral for UOSp(k_1/2k_2)

TL;DR

This paper proves the extension of the Harish--Chandra integral to the unitary orthosymplectic supergroup UOSp(k_1/2k_2) by constructing and solving an eigenvalue equation, confirming a longstanding conjecture.

Contribution

It provides the first rigorous proof of the supersymmetric Harish--Chandra integral for UOSp(k_1/2k_2), extending previous conjectures to all classical supergroups.

Findings

Confirmed the conjecture for UOSp(k_1/2k_2)

Constructed an eigenvalue equation for the supergroup

Solved the eigenvalue equation explicitly

Abstract

The previous supersymmetric generalization of the unitary Harish--Chandra integral prompted the conjecture that the Harish--Chandra formula should extend to all classical supergroups. We prove this conjecture for the unitary orthosymplectic supergroup UOSp(k_1/2k_2). To this end, we construct and solve an eigenvalue equation.