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
Number of pages	36
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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title = "Generalised Temperley-Lieb algebras of type G(r,1,n)",

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.",

keywords = "Cellular basis, Decomposition numbers, Hecke algebras, KLR algebras, Temperley-Lieb algebra",

author = "Gus Lehrer and Mengfan Lyu",

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year = "2023",

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language = "English",

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AU - Lehrer, Gus

AU - Lyu, Mengfan

PY - 2023/10

Y1 - 2023/10

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

UR - https://hdl.handle.net/1959.7/uws:75265

U2 - 10.1016/j.jpaa.2023.107402

DO - 10.1016/j.jpaa.2023.107402

M3 - Article

SN - 0022-4049

VL - 227

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 10

M1 - 107402

ER -

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

Abstract

Bibliographical note

Keywords

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