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## Abstract

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 language | English |
---|---|

Pages (from-to) | 2856-2883 |

Number of pages | 28 |

Journal | Linear and Multilinear Algebra |

Volume | 70 |

Issue number | 15 |

DOIs | |

State | Published - 2022 |

## Keywords

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

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