
Journal of Lie Theory 34 (2024), No. 3, 511530 Copyright Heldermann Verlag 2024 On The Stability of Tensor Product Representations of Classical Groups Dibyendu Biswas Indian Institute of Technology Bombay, Mumbai, India dibubis@gmail.com [Abstractpdf] \def\GL{{\rm GL}} From an irreducible representation of $\GL{(n,{\mathbb C})}$ there is a natural way to construct an irreducible representations of $\GL{(n+1,{\mathbb C})}$ by adding a zero at the end of the highest weight $\underline{\lambda} = ( \lambda_1 \geq \lambda_2 \geq \cdots \geq \lambda_n)$ with $\lambda_i \geq 0$ of the irreducible representation of $\GL{(n,{\mathbb C})}$. The paper considers the decomposition of tensor products of irreducible representation of $\GL{(n,{\mathbb C})}$ and of the corresponding irreducible representations of $\GL{(n+1,{\mathbb C})}$ and proves a stability result about such tensor products. We go on to discuss similar questions for classical groups. Keywords: Classical groups, tensor product, Pieri's rule, LittlewoodRichardson rule, Weyl character formula. MSC: 22E46, 20G05; 05E10. [ Fulltextpdf (166 KB)] for subscribers only. 