Dual pairs of group actions, generalizations of derivations, and noncommutative invariant theory

2015 Fiscal Year Final Research Report

• Project/Area Number: 24740021
• Research Category: Grant-in-Aid for Young Scientists (B)
• 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
• 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

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).

Free Research Field

不変式論