Geodesic
Doubly stochastic matrices and Schur-Weyl duality for partition algebras
Stephen Doty1
1Loyola University Chicago
The electronic journal of combinatorics, Tome 29 (2022) no. 4
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We prove that the permutations of $\{1,\dots, n\}$ having an increasing (resp., decreasing) subsequence of length $n-r$ index a subset of the set of all $r$th Kronecker powers of $n \times n$ permutation matrices which is a basis for the linear span of that set. Thanks to a known Schur-Weyl duality, this gives a new basis for the centralizer algebra of the partition algebra acting on the $r$th tensor power of a vector space. We give some related results on the set of doubly stochastic matrices in that algebra.
DOI : 10.37236/10831
Classification : 15B51, 05B20, 05E40, 05A05, 05A10, 20B30, 20C30, 20C08
Mots-clés : doubly stochastic matrix, permutation matrix, partition algebra, Birkhoff's theorem, Schur-Weyl duality, Kazhdan-Lusztig basis

Stephen Doty  1

1 Loyola University Chicago 
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     author = {Stephen Doty},
     title = {Doubly stochastic matrices and {Schur-Weyl} duality for partition algebras},
     journal = {The electronic journal of combinatorics},
     year = {2022},
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     doi = {10.37236/10831},
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Stephen Doty. Doubly stochastic matrices and Schur-Weyl duality for partition algebras. The electronic journal of combinatorics, Tome 29 (2022) no. 4. doi: 10.37236/10831

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