| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
In a course of a study of spin analog of K\"ulshammer-Olsson-Robinson theory (Invent.Math.,(2003)), we found and proved a new Rogers-Ramajujan type identity for each odd number $p\geq 3$ (joint work with Masaki Watanabe). When $p=3$, it is nothing but ``Schur partition theorem (1926)'' that you can find in almost all textbooks on the theory of partitions. When $p=5$, it is the same as the conjecture due to G.Andrews found in 1970s in a course of his 3 parameter generalization of the Rogers-Ramajujan identities. Andrews' conjecture was proved about 20 years later (Trans.A.M.S.,(1994)) with an aid of computers. Our generalization and proof are based on a theory of perfect crystals of Kyoto school and provides new insight into the theory of partitions (arXiv:1609.01905).
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