{
  "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
}