Cohomology and Decomposition of Tensor Product Representations of SL(2,R)

TL;DR

This paper investigates how tensor products of infinite-dimensional unitary and finite-dimensional non-unitary representations of SL(2,R) decompose, providing explicit formulas with cohomological considerations.

Contribution

It introduces explicit decomposition formulas for tensor products of SL(2,R) representations, incorporating cohomological reductions, which advances understanding of their structure.

Findings

Derived explicit decomposition formulas for tensor products

Incorporated cohomological reduction into the decomposition process

Extended classical results to infinite-dimensional representation contexts

Abstract

We analyze the decomposition of tensor products between infinite dimensional (unitary) and finite-dimensional (non-unitary) representations of SL(2,R). Using classical results on indefinite inner product spaces, we derive explicit decomposition formulae, true modulo a natural cohomological reduction, for the tensor products.