| Budget Amount *help |
¥16,250,000 (Direct Cost: ¥12,500,000、Indirect Cost: ¥3,750,000)
Fiscal Year 2018: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2017: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2016: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2015: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2014: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
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| Outline of Final Research Achievements |
In the first half of the research period, we have developed and polished the theory of geometric extension algebras from the both of the general theory and examples like quiver Hecke algebras and generalized Springer correspondence. In particulcar, we have revealed that quiver Hecke algebras possesses a structure similar to the classical theory of highest weight categories, and find that the orthogonality relation of Green functions arising from representation theory of Chevalley groups are direct corollaries of some orthogonality in the sense of homological algebras. This resolves several conjectures in this area.
In the latter half, we have studied the representation theory of current algebras and geometry of semi-infinite flag manifolds and affine Grassmanians. Although the setting is different, the pattern is similar here. Consequently we have proved several conjectures also in this area.
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