Skew Howe duality and random rectangular Young tableaux
Algebraic Combinatorics, Volume 1 (2018) no. 1, p. 81-94
We consider the decomposition into irreducible components of the external power p ( m n ) regarded as a GL m ×GL n -module. Skew Howe duality implies that the Young diagrams from each pair (λ,μ) which contributes to this decomposition turn out to be conjugate to each other, i.e. μ=λ ' . We show that the Young diagram λ which corresponds to a randomly selected irreducible component (λ,λ ' ) has the same distribution as the Young diagram which consists of the boxes with entries p of a random Young tableau of rectangular shape with m rows and n columns. This observation allows treatment of the asymptotic version of this decomposition in the limit as m,n,p tend to infinity.
Received : 2017-08-07
Revised : 2017-09-21
Accepted : 2017-11-17
Published online : 2018-01-29
DOI : https://doi.org/10.5802/alco.8
Classification:  22E46,  20C30,  60C05
Keywords: Skew Howe duality, random Young diagrams, representations of general linear groups GL m , representations of finite symmetric groups
@article{ALCO_2018__1_1_81_0,
     author = {Panova, Greta and {\'S}niady, Piotr},
     title = {Skew Howe duality and random rectangular Young tableaux},
     journal = {Algebraic Combinatorics},
     publisher = {MathOA foundation},
     volume = {1},
     number = {1},
     year = {2018},
     pages = {81-94},
     doi = {10.5802/alco.8},
     zbl = {06882335},
     language = {en},
     url = {http://alco.centre-mersenne.org/item/ALCO_2018__1_1_81_0}
}
Panova, Greta;Śniady, Piotr. Skew Howe duality and random rectangular Young tableaux. Algebraic Combinatorics, Volume 1 (2018) no. 1, p. 81-94. doi : 10.5802/alco.8. https://alco.centre-mersenne.org/item/ALCO_2018__1_1_81_0/

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