| Budget Amount *help |
¥13,650,000 (Direct Cost: ¥10,500,000、Indirect Cost: ¥3,150,000)
Fiscal Year 2020: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2019: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2018: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2017: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2016: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
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| Outline of Final Research Achievements |
Semi-infinite flag manifolds are infinite-dimensional algebraic varieties associated to complex simple algebraic groups; the torus-equivariant K-group of a semi-infinite flag manifold is isomorphic to the torus-equivariant quantum K-theory of a finite-dimensional flag manifold.
We revealed a close relation between the torus-equivariant K-group of semi-infinite flag manifolds and the theory of level-zero modules over quantum affine algebras. Moreover, on the basis of this relation, we proved a Chevalley formula for the torus-equivariant K-group of semi-infinite flag manifolds, which describes the tensor product with the line bundle class associated to an arbitrary integral weight; this was achieved by establishing an explicit identity for the graded characters of level-zero Demazure modules over quantum affine algebras. Note that our Chevalley formula is described in terms of the quantum alcove model, which is a uniform combinatorial model in combinatorial representation theory.
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