| Budget Amount *help |
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2003: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2002: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Research Abstract |
The goal of this research is to study the modular representations of Hecke algebras of classical type, by using methods of Artin algebras. As the general theory of Artin algebras does not suffice to obtain concrete results for the Hecke algebras, the idea was to use my previous result, which allows us to compute the decomposition numbers of Hecke algebras of classical type (type B in particular), jointly with the general theory of Artin algebras.
After two years of research, we have obtained satisfactory results for the determination of representation types of the Hecke algebras. Main result is as follows.
Theorem. Let W be a Weyl group, Pw(x) be the Poincare polynomial of W, F an algebraically closed field, q ∈ F so that q ≠ 0,1. The associated Hecke algebra, which is an F-algebra, is denoted by Hw(q). Then, Hw(q) is finite, tame, wild if (x-q)^2 does not divide Pw(x), q = -1 ≠ 1 and (x + 1)^2 ‖ Pw(x) otherwise, respectively.
We also have the result for two parameter Hecke algebras in type B case.
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