| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
We study the semi-infinite Bruhat order on an affine Weyl group by using semi-infinite Lakshmibai-Seshadri paths. We introduce the crystal of semi-infinite Young tableaux, and show that it is isomorphic to the crystal basis of an extremal weight module over a quantum affine algebra of type A. We give a tableau criterion for the semi-infinite Bruhat order on an affine Weyl group of classical type. Also, we consider a generalization of (semi-infinite) Lakshmibai-Seshadri paths in connection with the crystal bases of extremal weight modules over a quantized universal enveloping algebra associated with a symmetrizable Kac-Moody Lie algebra.
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