Higher Ext-groups in the triple product case

TL;DR

This paper computes higher extension groups for irreducible representations and derives a multiplicity formula for finite length representations in the context of triple products, advancing understanding in representation theory.

Contribution

It introduces explicit calculations of higher Ext-groups and a new multiplicity formula for triple product representations, filling gaps in the existing theory.

Findings

Computed higher extension groups for all irreducible representations.

Derived a multiplicity formula for finite length representations in triple product cases.

Enhanced understanding of the structure of representations in triple product scenarios.

Abstract

In this short note, we compute higher extension groups for all irreducible representations and deduce the multiplicity formula for finite length representations in triple product case.