On The Stability of Tensor Product Representations of Classical Groups
Journal of Lie Theory, Tome 34 (2024) no. 3, pp. 511-530
Voir la notice de l'article provenant de la source Heldermann Verlag
\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.
Classification :
22E46, 20G05, 05E10
Mots-clés : Classical groups, tensor product, Pieri's rule, Littlewood-Richardson rule, Weyl character formula
Mots-clés : Classical groups, tensor product, Pieri's rule, Littlewood-Richardson rule, Weyl character formula
Affiliations des auteurs :
Dibyendu Biswas 1
Dibyendu Biswas. On The Stability of Tensor Product Representations of Classical Groups. Journal of Lie Theory, Tome 34 (2024) no. 3, pp. 511-530. http://geodesic.mathdoc.fr/item/JOLT_2024_34_3_a1/
@article{JOLT_2024_34_3_a1,
author = {Dibyendu Biswas},
title = {On {The} {Stability} of {Tensor} {Product} {Representations} of {Classical} {Groups}},
journal = {Journal of Lie Theory},
pages = {511--530},
year = {2024},
volume = {34},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2024_34_3_a1/}
}