| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| 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.
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