Crystal base, typical demonstration base and modular representation theory

Ontology type: schema:MonetaryGrant

Grant Info

YEARS

2007-2010

FUNDING AMOUNT

200000 CNY

ABSTRACT

We show that the generalised Dipper-James-Murphy conjecture is true in the case when e=0 or the multipartitions in questions are multi-cores. As a result, we obtain some non-recursive characterizations of Kleshchev multipartitions in these cases; We give a Morita equivalence theorem for the cyclotomic Hecke algebras of type G(r,p,n) and show that computing their decomposition numbers reduces to computing the p-splittable decomposition numbers and the case when the parameters are in a single (\epsilon,q)-orbit. In the case of type D_n and when the parameter q satisfies the separation condition, we get some explicit equalities which relate its decomposition numbers with certain Schur elements and the decomposition numbers of various Iwahori-Hecke algebras of type A. When char K = 0,this completely determines all of its decomposition numbers; We set up connections between two parameterizations of simple modules over the cyclotomic Hecke algebras of type G(r,p,n): the one using Kleshchev multipartitions and the one using FLOTW r-partitions, and we derive closed formulae for the number of simple modules over these Hecke algebras; Using Kashiwara-Lusztig's crystal and canonical bases theory, we prove that the space of partially harmonic tensors of type C has a Weyl filtration and is stable under base change and we obt More... »

URL

http://npd.nsfc.gov.cn/projectDetail.action?pid=10771014

Identifiers

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