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

Hau Wen Huang

doi:10.1080/03081087.2020.1817297

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

Hau Wen Huang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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	https://doi.org/10.1080/03081087.2020.1817297
State	Published - 2022

Keywords

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

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10.1080/03081087.2020.1817297

The Unversial Racah Algebra and Its Applications(3/4)
Huang, H.-W. (PI)
1/08/19 → 31/07/20
Project: Research

Cite this

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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.",

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AU - Huang, Hau Wen

PY - 2022

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N2 - 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.

AB - 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.

KW - 20C08

KW - 33D45

KW - 33D80

KW - Double affine Hecke algebras

KW - irreducible modules

KW - universal property

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M3 - 期刊論文

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SN - 0308-1087

VL - 70

SP - 2856

EP - 2883

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

IS - 15

ER -

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

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Keywords

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The Unversial Racah Algebra and Its Applications(3/4)

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