Graded decomposition matrices of $v$-Schur algebras via Jantzen filtration
نویسندگان
چکیده
منابع مشابه
GRADED 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 کاملOn decomposition numbers with Jantzen filtration of cyclotomic q-Schur algebras
Let S (Λ) be the cyclotomic q-Schur algebra associated to the ArikiKoike algebra Hn,r, introduced by Dipper-James-Mathas. In this paper, we consider v-decomposition numbers of S (Λ), namely decomposition numbers with respect to the Jantzen filtrations of Weyl modules. We prove, as a v-analogue of the result obtained by Shoji-Wada, a product formula for v-decomposition numbers of S (Λ), which as...
متن کاملGRADED q-SCHUR ALGEBRAS
Generalizing recent work of Brundan and Kleshchev, we introduce grading on Dipper-James’ q-Schur algebra, and prove a graded analogue of the Leclerc and Thibon’s conjecture on the decomposition numbers of the q-Schur algebra.
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.
متن کاملAnother runner removal theorem for v-decomposition numbers of Iwahori–Hecke algebras and q-Schur algebras
Let F denote the Fock space representation of the quantum groupUv(ŝle). The ‘v-decomposition numbers’ are the coefficients when the canonical basis for this representation is expanded in terms of the basis of partitions, and the evaluations at v = 1 of these polynomials give the decomposition numbers for Iwahori–Hecke algebras and q-Schur algebras over C. James and Mathas have proved a theorem ...
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ژورنال
عنوان ژورنال: Representation Theory of the American Mathematical Society
سال: 2012
ISSN: 1088-4165
DOI: 10.1090/s1088-4165-2012-00416-2