{
  "annotation_id": "f8d4f72e-d3ac-4610-85b4-fc07d28cfed6",
  "date_created": "2026-03-02T18:01:28.138000Z",
  "date_modified": "2026-03-02T18:01:28.138000Z",
  "file_hash": "eb7c28c181dd6e548e92cd03e6eced7d07606f87f50a6ee983bc248551e88708",
  "private": false,
  "record": {
    "abstract": "In this paper we construct examples of commutative rings of difference\noperators with matrix coefficients from representation theory of quantum\ngroups, generalizing the results of our previous paper to the $q$-deformed\ncase. A generalized Baker-Akhiezer function $\\Psi$ is realized as a matrix\ncharacter of a Verma module and is a common eigenfunction for a commutative\nring of difference operators. In particular, we obtain the following result in\nMacdonald theory: at integer values of the Macdonald parameter $k$, there exist\ndifference operators commuting with Macdonald operators which are not\npolynomials of Macdonald operators. This result generalizes an analogous result\nof Chalyh and Veselov for the case $q=1$, to arbitrary $q$. As a by-product, we\nprove a generalized Weyl character formula for Macdonald polynomials (a\nconjecture by G.Felder and A.Varchenko), the duality for the $\\Psi$-function,\nand the existence of shift operators.",
    "arxiv_id": "q-alg/9603022",
    "authors": [
      "Pavel Etingof",
      "Konstantin Styrkas"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Algebraic integrability of Macdonald operators and representations of   quantum groups",
    "url": "https://arxiv.org/abs/q-alg/9603022"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "83d7a65f-4450-4f7c-bc46-b0f2c44ad374",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}