dorsal/arxiv
View SchemaA Littlewood-Richardson filtration at roots of 1 for multiparameter deformations of skew Schur modules.
| Authors | G. Boffi, M. Varagnolo |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9501002 |
| URL | https://arxiv.org/abs/q-alg/9501002 |
Abstract
Let R be a commutative ring, q a unit of R and P a multiplicatively antisymmetric matrix with coefficients which are integers powers of q. Denote by SE(q,P) the multiparameter quantum matrix bialgebra associated to q and P.Slightly generalizing [Hashimoto-Hayashi,Tohoku Math.Tohoku Math.J. 44(1992)],we define a multiparameter deformation $L_{\l/\mu}V_P$ of the classical skew Schur module.In case R is a field and q is not a root of 1, arguments like those given in [H-H] show that $L_{\l/\mu}V_P$ is irreducible and its decomposition into irreducibles is $\sum_\nu c(\l/\mu;\nu)L_\nu V_P$ where the coefficients are the usual Littlewood-Richardson ones. When R is any ring and q is allowed to be a root of 1, we construct a filtration of $L_{\l/\mu}V_P$ as an SE(q,P)-comodule, such that its associated graded object is precisely $\sum_\nu c(\l/\mu;\nu)L_\nu V_P$.
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"date_created": "2026-03-02T18:01:24.908000Z",
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"abstract": "Let R be a commutative ring, q a unit of R and P a multiplicatively\nantisymmetric matrix with coefficients which are integers powers of q. Denote\nby SE(q,P) the multiparameter quantum matrix bialgebra associated to q and\nP.Slightly generalizing [Hashimoto-Hayashi,Tohoku Math.Tohoku Math.J.\n44(1992)],we define a multiparameter deformation $L_{\\l/\\mu}V_P$ of the\nclassical skew Schur module.In case R is a field and q is not a root of 1,\narguments like those given in [H-H] show that $L_{\\l/\\mu}V_P$ is irreducible\nand its decomposition into irreducibles is $\\sum_\\nu c(\\l/\\mu;\\nu)L_\\nu V_P$\nwhere the coefficients are the usual Littlewood-Richardson ones. When R is any\nring and q is allowed to be a root of 1, we construct a filtration of\n$L_{\\l/\\mu}V_P$ as an SE(q,P)-comodule, such that its associated graded object\nis precisely $\\sum_\\nu c(\\l/\\mu;\\nu)L_\\nu V_P$.",
"arxiv_id": "q-alg/9501002",
"authors": [
"G. Boffi",
"M. Varagnolo"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "A Littlewood-Richardson filtration at roots of 1 for multiparameter deformations of skew Schur modules.",
"url": "https://arxiv.org/abs/q-alg/9501002"
},
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