A conjecture for q-decomposition matrices of cyclotomic v-Schur algebras
نویسندگان
چکیده
منابع مشابه
On decomposition numbers of the cyclotomic q-Schur algebras
Let S(Λ) be the cyclotomic q-Schur algebra associated to the ArikiKoike algebra H . We construct a certain subalgebra S(Λ) of S(Λ), and show that it is a standardly based algebra in the sense of Du and Rui. S(Λ) has a natural quotient S(Λ), which turns out to be a cellular algebra. In the case where the modified Ariki-Koike algebra H ♭ is defined, S(Λ) coincides with the cyclotomic q-Schur alge...
متن کاملPresenting 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 کاملGRADED DECOMPOSITION MATRICES OF v-SCHUR ALGEBRAS VIA JANTZEN FILTRATION
We prove that certain parabolic Kazhdan-Lusztig polynomials calculate the graded decomposition matrices of v-Schur algebras given by the Jantzen filtration of Weyl modules, confirming a conjecture of Leclerc and Thibon.
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: 2006
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2006.03.048