dorsal/arxiv
View SchemaThe Affine q-Schur algebra
| Authors | R. M. Green |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9705015 |
| URL | https://arxiv.org/abs/q-alg/9705015 |
Abstract
We introduce an analogue of the $q$-Schur algebra associated to Coxeter systems of type $\hat A_{n-1}$. We give two constructions of this algebra. The first construction realizes the algebra as a certain endomorphism algebra arising from an affine Hecke algebra of type $\hat A_{r-1}$, where $n \geq r$. This generalizes the original $q$-Schur algebra as defined by Dipper and James, and the new algebra contains the ordinary $q$-Schur algebra and the affine Hecke algebra as subalgebras. Using this approach we can prove a double centralizer property. The second construction realizes the affine $q$-Schur algebra as the faithful quotient of the action of a quantum group on the tensor power of a certain module, analogous to the construction of the ordinary $q$-Schur algebra as a quotient of $U(\frak g \frak l_n)$.
{
"annotation_id": "0220ec6c-6db1-42d3-9e47-68f94590e759",
"date_created": "2026-03-02T18:01:27.730000Z",
"date_modified": "2026-03-02T18:01:27.730000Z",
"file_hash": "a608f97afef42782ef5b8c6e3273bbd92ed2ac5e86d03d69dc881b58ee250513",
"private": false,
"record": {
"abstract": "We introduce an analogue of the $q$-Schur algebra associated to Coxeter\nsystems of type $\\hat A_{n-1}$. We give two constructions of this algebra. The\nfirst construction realizes the algebra as a certain endomorphism algebra\narising from an affine Hecke algebra of type $\\hat A_{r-1}$, where $n \\geq r$.\nThis generalizes the original $q$-Schur algebra as defined by Dipper and James,\nand the new algebra contains the ordinary $q$-Schur algebra and the affine\nHecke algebra as subalgebras. Using this approach we can prove a double\ncentralizer property. The second construction realizes the affine $q$-Schur\nalgebra as the faithful quotient of the action of a quantum group on the tensor\npower of a certain module, analogous to the construction of the ordinary\n$q$-Schur algebra as a quotient of $U(\\frak g \\frak l_n)$.",
"arxiv_id": "q-alg/9705015",
"authors": [
"R. M. Green"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "The Affine q-Schur algebra",
"url": "https://arxiv.org/abs/q-alg/9705015"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "e4ceb09a-9d01-4ea7-aacf-82bab64b161b",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}