On a Convexity Property of Tensor Products of Irreducible, Rational Representations of SL(n)

H. Narayanan; C. S. Rajan

doi:10.5802/jolt.1218

H. Narayanan; C. S. Rajan

Journal of Lie Theory, Volume 32 (2022) no. 1, pp. 23-28

Abstract

The aim of this note is to point out a convexity property with respect to the root lattice for the support of the highest weights that occur in a tensor product of irreducible rational representations of SL(n) (or more generally any Lie group over which the saturation property holds) over the complex numbers. The observation is a consequence of the convexity properties of the saturation cone and the validity of the saturation conjecture for SL(n).

arXiv Zbl

DOI: 10.5802/jolt.1218

Classification: 20G05, 22E45, 05E10
Keywords: Tensor products, SL(n), convexity

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     title = {On a {Convexity} {Property} of {Tensor} {Products} of {Irreducible,} {Rational} {Representations} of {SL(n)}},
     journal = {Journal of Lie Theory},
     pages = {23--28},
     year = {2022},
     volume = {32},
     number = {1},
     doi = {10.5802/jolt.1218},
     zbl = {1487.14102},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1218/}
}

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H. Narayanan; C. S. Rajan. On a Convexity Property of Tensor Products of Irreducible, Rational Representations of SL(n). Journal of Lie Theory, Volume 32 (2022) no. 1, pp. 23-28. doi: 10.5802/jolt.1218

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