| Budget Amount *help |
¥17,940,000 (Direct Cost: ¥13,800,000、Indirect Cost: ¥4,140,000)
Fiscal Year 2016: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2015: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2014: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2013: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2012: ¥7,670,000 (Direct Cost: ¥5,900,000、Indirect Cost: ¥1,770,000)
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| Outline of Final Research Achievements |
We study various aspects of algebraic combinatorics related to plane partitions and alternating sign matrices. 1. We establish Pfaffian analogues of the Cauchy-Binet formula and prove several identities among Schur Q-functions and their generalizations. 2. We prove the generating function for Young books can be written as a q-Selberg-type integral. 3. By establishing Pieri rules for classical groups, we give another proof to Burrill's conjecture and find its generalizations. 4. We find Giambelli-type determinant identities for the expansion coefficients of the \tau-function of the KP hierarchy, and prove that these determinant identities characterize solutions of the KP hierarchy.
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