| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Research Abstract |
Representation theory of affine Hecke algebras and KLR algebras are important in many aspect. I find and proved that they possess many families of standard modules whose properties are reminicent to these in the theory of quasi-hereditary algebras. In particular, they satisfies the some kind of ``orthogonality property". Such an orthogonality property (and some ordering on irreducible representations) determines the characters, and seems to capture the orthogonality of characters in more primitive fashion.
As applications, we proved the finiteness of the global dimension of KLR algebras (a question raised by Kashiwara), and the positivity of the transition matrix between canonical/global bases and PBW bases (a conjecture of Lusztig).
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