| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
We studied invariant theory for exterior algebras. One of the main results is some anticommuting analogues of the Cayley-Hamilton theorem, which are closely related to Amitsur-Levitzki type theorems. We also obtained a new matrix function named the "twisted immanant," and found its interesting properties.
Moreover, we gave a q-analogue of derivations on tensor algebras. Using these derivations, we can describe the natural action of the quantum enveloping algebra U_q(GL(V)) on T_n(V). Furthermore, we obtained a new proof of the q-Schur-Weyl duality (the duality between U_q(GL(V)) and the Iwahori-Hecke algebra of type A).
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