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On the stability of tensor product of representations of classical groups · arXivDesk

2207.05809Jul 12, 2022This is a revised version of the previous submission in which we prove the result of tensor product decomposition just before stability

On the stability of tensor product of representations of classical groups

Dibyendu Biswas

Representation Theory

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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.

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The paper addresses: On the stability of tensor product of representations of classical groups.
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).

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Author comment: This is a revised version of the previous submission in which we prove the result of tensor product decomposition just before stability