Generalised Temperley-Lieb algebras of type G(r,1,n)

Gus Lehrer; Mengfan Lyu

doi:10.1016/j.jpaa.2023.107402

Generalised Temperley-Lieb algebras of type G(r,1,n)

Gus Lehrer, Mengfan Lyu

University of Sydney

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

1 Citation (Scopus)

Abstract

In this paper, we define a quotient of the cyclotomic Hecke algebra of type G(r,1,n) as a generalisation of the Temperley-Lieb algebras of type A and B. We establish a graded cellular structure for the generalised Temperley-Lieb algebra and, using the technology of KLR algebras, determine the corresponding decomposition matrix.

Original language	English
Article number	107402
Journal	Journal of Pure and Applied Algebra
Volume	227
Issue number	10
DOIs	https://doi.org/10.1016/j.jpaa.2023.107402
Publication status	Published - Oct 2023
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2023 Elsevier B.V.

Keywords

Cellular basis
Decomposition numbers
Hecke algebras
KLR algebras
Temperley-Lieb algebra

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10.1016/j.jpaa.2023.107402

Cite this

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abstract = "In this paper, we define a quotient of the cyclotomic Hecke algebra of type G(r,1,n) as a generalisation of the Temperley-Lieb algebras of type A and B. We establish a graded cellular structure for the generalised Temperley-Lieb algebra and, using the technology of KLR algebras, determine the corresponding decomposition matrix.",

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N2 - In this paper, we define a quotient of the cyclotomic Hecke algebra of type G(r,1,n) as a generalisation of the Temperley-Lieb algebras of type A and B. We establish a graded cellular structure for the generalised Temperley-Lieb algebra and, using the technology of KLR algebras, determine the corresponding decomposition matrix.

AB - In this paper, we define a quotient of the cyclotomic Hecke algebra of type G(r,1,n) as a generalisation of the Temperley-Lieb algebras of type A and B. We establish a graded cellular structure for the generalised Temperley-Lieb algebra and, using the technology of KLR algebras, determine the corresponding decomposition matrix.

KW - Cellular basis

KW - Decomposition numbers

KW - Hecke algebras

KW - KLR algebras

KW - Temperley-Lieb algebra

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ER -

Generalised Temperley-Lieb algebras of type G(r,1,n)

Abstract

Bibliographical note

Keywords

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