Finite-dimensional irreducible modules of the universal DAHA of type (C 1,C 1)

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Assume that (Formula presented.) is an algebraically closed field and let q denote a nonzero scalar in (Formula presented.) that is not a root of unity. The universal DAHA (double affine Hecke algebra) (Formula presented.) of type (Formula presented.) is an unital associative (Formula presented.) -algebra defined by generators and relations. The generators are (Formula presented.) and the relations assert that (Formula presented.) In this paper we describe the finite-dimensional irreducible (Formula presented.) -modules from many viewpoints and classify the finite-dimensional irreducible (Formula presented.) -modules up to isomorphism. The proofs are carried out in the language of linear algebra.

Original languageEnglish
Pages (from-to)2856-2883
Number of pages28
JournalLinear and Multilinear Algebra
Issue number15
StatePublished - 2022


  • 20C08
  • 33D45
  • 33D80
  • Double affine Hecke algebras
  • irreducible modules
  • universal property


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