Journal of Lie Theory 34 (2024), No. 3, 511--530
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
[Abstract-pdf]
\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, Littlewood-Richardson rule, Weyl character formula.
MSC: 22E46, 20G05; 05E10.
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