Dual pairs of group actions, generalizations of derivations, and noncommutative invariant theory
Project/Area Number |
24740021
|
Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Algebra
|
Research Institution | Kagoshima University |
Principal Investigator |
Itoh Minoru 鹿児島大学, 理工学域理学系, 准教授 (60381141)
|
Project Period (FY) |
2012-04-01 – 2016-03-31
|
Project Status |
Completed (Fiscal Year 2015)
|
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)
|
Keywords | 不変式論 / 外積代数 / テンソル代数 / Cayley-Hamilton定理 / Amitsur-Levitzki定理 / Schur-Weyl双対性 / immanant / Capelli恒等式 / 量子展開環 / Iwahori-Hecke代数 / 不変式論の第二基本定理 / トレース付き代数 |
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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Report
(5 results)
Research Products
(17 results)