منابع مشابه
Presenting cyclotomic q-Schur algebras
We give a presentation of cyclotomic q-Schur algebras by generators and defining relations. As an application, we give an algorithm for computing decomposition numbers of cyclotomic q-Schur algebras. § 0. Introduction Let Hn,r be an Ariki-Koike algebra associated to a complex reflection group Sn ⋉ (Z/rZ). A cyclotomic q-Schur algebra Sn,r associated to Hn,r, introduced in [DJM], is defined as a...
متن کاملCYCLOTOMIC q-SCHUR ALGEBRAS AND SCHUR-WEYL DUALITY
The representation theory of Hecke algebras has been an important part toward understanding (ordinary or modular) representation theories of finite groups of Lie type. Schur algebras, as endomorphism algebras, connects the representation theory of general linear groups and the representations of symmetric groups via Schur-Weyl duality. The quantum version of Schur-Weyl duality is established by...
متن کاملCYCLOTOMIC q-SCHUR ALGEBRAS ASSOCIATED TO THE ARIKI-KOIKE ALGEBRA
Let Hn,r be the Ariki-Koike algebra associated to the complex reflection group Sn (Z/rZ)n, and let S(Λ) be the cyclotomic q-Schur algebra associated to Hn,r, introduced by Dipper, James and Mathas. For each p = (r1, . . . , rg) ∈ Zg>0 such that r1 + · · · + rg = r, we define a subalgebra Sp of S(Λ) and its quotient algebra S. It is shown that Sp is a standardly based algebra and S is a cellular...
متن کاملThe representation type of cyclotomic q-Schur algebras
We give a necessary and sufficient condition on parameters for cyclotomic q-Schur algebras to be of finite representation type.
متن کاملTHE JANTZEN SUM FORMULA FOR CYCLOTOMIC q–SCHUR ALGEBRAS
The cyclotomic q-Schur algebra was introduced by Dipper, James and Mathas, in order to provide a new tool for studying the Ariki-Koike algebra. We here prove an analogue of Jantzen’s sum formula for the cyclotomic q-Schur algebra. Among the applications is a criterion for certain Specht modules of the Ariki-Koike algebras to be irreducible.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2019
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2019.06.024