Canonical basic sets in type B-n

Meinolf Josef Geck; Nicolas Jacon

doi:10.1016/j.jalgebra.2006.03.042

Canonical basic sets in type B-n

Meinolf Josef Geck, Nicolas Jacon

Mathematical Science

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13 Citations (Scopus)

Abstract

More than 10 years ago, Dipper, James and Murphy developed the theory of Specht modules for Hecke algebras of type B-n More recently, using Lusztig's a-function, Geck and Rouquier showed how to obtain parametrizations of the irreducible representations of Hecke algebras (of any finite type) in terms of socalled canonical basic sets. For certain values of the parameters in type B-n combinatorial descriptions of these basic sets were found by Jacon, based on work of Ariki and Foda-Leclerc-Okado-Thibon-Weish. Here, we consider the canonical basic sets for all the remaining choices of the parameters. (c) 2006 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	104-127
Number of pages	24
Journal	Journal of Algebra
Volume	306
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2006.03.042
Publication status	Published - Dec 2006

Keywords

Ariki-Koike algebras
cyclotomic Hecke algebras
smple modules
representations
roots
unity
bases

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10.1016/j.jalgebra.2006.03.042

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title = "Canonical basic sets in type B-n",

abstract = "More than 10 years ago, Dipper, James and Murphy developed the theory of Specht modules for Hecke algebras of type B-n More recently, using Lusztig's a-function, Geck and Rouquier showed how to obtain parametrizations of the irreducible representations of Hecke algebras (of any finite type) in terms of socalled canonical basic sets. For certain values of the parameters in type B-n combinatorial descriptions of these basic sets were found by Jacon, based on work of Ariki and Foda-Leclerc-Okado-Thibon-Weish. Here, we consider the canonical basic sets for all the remaining choices of the parameters. (c) 2006 Elsevier Inc. All rights reserved.",

keywords = "Ariki-Koike algebras, cyclotomic Hecke algebras, smple modules, representations, roots, unity, bases",

author = "Geck, {Meinolf Josef} and Nicolas Jacon",

year = "2006",

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T1 - Canonical basic sets in type B-n

AU - Geck, Meinolf Josef

AU - Jacon, Nicolas

PY - 2006/12

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AB - More than 10 years ago, Dipper, James and Murphy developed the theory of Specht modules for Hecke algebras of type B-n More recently, using Lusztig's a-function, Geck and Rouquier showed how to obtain parametrizations of the irreducible representations of Hecke algebras (of any finite type) in terms of socalled canonical basic sets. For certain values of the parameters in type B-n combinatorial descriptions of these basic sets were found by Jacon, based on work of Ariki and Foda-Leclerc-Okado-Thibon-Weish. Here, we consider the canonical basic sets for all the remaining choices of the parameters. (c) 2006 Elsevier Inc. All rights reserved.

KW - Ariki-Koike algebras

KW - cyclotomic Hecke algebras

KW - smple modules

KW - representations

KW - roots

KW - unity

KW - bases

U2 - 10.1016/j.jalgebra.2006.03.042

DO - 10.1016/j.jalgebra.2006.03.042

M3 - Article

SN - 0021-8693

VL - 306

SP - 104

EP - 127

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -

Canonical basic sets in type B-n

Abstract

Keywords

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