Journal of Lie Theory

no. 3
On The Stability of Tensor Product Representations of Classical Groups
Journal of Lie Theory, Volume 34 (2024) no. 3, pp. 511-530
\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.
DOI: 10.5802/jolt.1347
Classification: 22E46, 20G05, 05E10
Keywords: Classical groups, tensor product, Pieri's rule, Littlewood-Richardson rule, Weyl character formula 
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     author = {D. 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},
     doi = {10.5802/jolt.1347},
     zbl = {1569.22015},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1347/}
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D. Biswas. On The Stability of Tensor Product Representations of Classical Groups. Journal of Lie Theory, Volume 34 (2024) no. 3, pp. 511-530. doi: 10.5802/jolt.1347

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