RSK bases and Kazhdan-Lusztig cells

Raghavan, K. N.; Pierre, Samuel; Subrahmanyam, K. V.

doi:10.5802/aif.2687

Cited by 3 publications

(1 citation statement)

References 17 publications

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“…Thus we obtain a new insight into a classical problem. Our result should be of interest even in the classical semisimple situation k = C (or any field of characteristic zero) considered by Weyl. We believe that the use of the word "canonical" to describe the bases in Theorem 2 is justified by the origins of these bases in the papers [RSS12,Dot21], where it was shown that they arise as leading terms of certain Kazhdan-Lusztig basis elements, complementary to a Kazhdan-Lusztig basis (evaluated at 1) for the ideal of relations in the second fundamental theorem. Those results depend very much on the Iwahori-Hecke algebras of type A.…”

Section: Introductionmentioning

confidence: 99%

Canonical bases and new applications of increasing and decreasing subsequences to invariant theory

Bowman¹,

Doty²,

Martin³

2022

Preprint

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Recent results show that the Kazhdan-Lusztig basis for Iwahori-Hecke algebras in type A provide "canonical" bases for the centralizer algebras of the Schur algebra and the partition algebra acting on tensor space. We exploit these bases to show that the linear decomposition of an arbitrary invariant (in the appropriate centraliser algebra) depends integrally on its entries, and describe combinatorial rules that pick out such entries.

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Section: Introductionmentioning

confidence: 99%

Canonical bases and new applications of increasing and decreasing subsequences to invariant theory

Bowman¹,

Doty²,

Martin³

2022

Preprint

View full text Add to dashboard Cite

show abstract

Canonical bases and new applications of increasing and decreasing subsequences to invariant theory

Bowman,

Doty,

Martin

2024

Journal of Algebra

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Doubly Stochastic Matrices and Schur-Weyl Duality for Partition Algebras

Doty

2022

Electron. J. Combin.

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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.

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RSK bases and Kazhdan-Lusztig cells

Cited by 3 publications

References 17 publications

Canonical bases and new applications of increasing and decreasing subsequences to invariant theory

Canonical bases and new applications of increasing and decreasing subsequences to invariant theory

Canonical bases and new applications of increasing and decreasing subsequences to invariant theory

Doubly Stochastic Matrices and Schur-Weyl Duality for Partition Algebras

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