Invariant trilinear forms for spherical degenerate principal series of complex symplectic groups

TL;DR

This paper computes specific integrals related to complex symplectic groups by analyzing intertwining operators within their principal series representations.

Contribution

It introduces a method to evaluate Bernstein-Reznikov integrals for complex symplectic groups using Knapp-Stein intertwining operators.

Findings

Explicit formulas for Bernstein-Reznikov integrals obtained.

New connections established between integrals and representation theory.

Enhanced understanding of degenerate principal series representations.

Abstract

We compute generalized Bernstein-Reznikov integrals associated with standard complex symplectic forms by studying Knapp-Stein intertwining operators between spherical degenerate principal series of complex symplectic groups.