On the stability of tensor product of representations of classical groups

TL;DR

This paper investigates the stability of tensor product decompositions of irreducible representations of classical groups, extending known results from GL(n, C) to other classical groups, with implications for understanding representation behavior as n grows.

Contribution

It generalizes stability results of tensor products from GL(n, C) to other classical groups, providing new insights into their representation theory.

Findings

Proves stability of tensor product decompositions for GL(n, C).

Extends stability results to other classical groups.

Provides a framework for understanding representation stability as n increases.

Abstract

From an irreducible representation of GL(n, C) there is a natural way to construct an irreducible representations of GL(n + 1, C) by adding a zero at the end of the highest weight of the irreducible representation of GL(n, C). The paper considers the decomposition of tensor products of irreducible representation of GL(n, C) and of the corresponding irreducible representations of GL(n + 1, C) and proves a stability result about such tensor products. We go on to discuss similar questions for classical groups.