Modular representation theory of Hecke algebras associated with complex reflection groups and their quasi-hereditary covers

2015 Fiscal Year Final Research Report

• Project/Area Number: 24740007
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Shinshu University
• Principal Investigator: WADA Kentaro 信州大学, 学術研究院理学系, 助教 (60583862)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 表現論 / Hecke 環 / Lie 環 / 量子群 / 複素鏡映群 / 組み合わせ論

Outline of Final Research Achievements

We studied on the representation theory of cyclotomic q-Schur algebras which are quasi-hereditary covers of cyclotomic Hecke algebras associated with complex reflection groups of type G(r,1,n).
In this research, we introduced the deformed current Lie algebra which is a filtered deformation of the current Lie algebra of the general linear Lie algebra, and also introduced the quantum deformed current algebra which is regarded as a q-analogue of the universal enveloping algebra of the deformed current Lie algebra. Then, we proved that the cyclotomic q-Schur algebra is a quotient algebra of the quantum deformed current algebra (in the case where q=1, the cyclotomic q-Schur algebra is a quotient of the universal enveloping algebra of the deformed current Lie algebra). Moreover, we gave some basic facts on representation theory of deformed current Lie algebras and quantum deformed current algebras.

Free Research Field

表現論