Quantum Howe duality and invariant polynomials

被引：2

作者：

Futorny, Vyacheslav ^{[1
]}

Krizka, Libor ^{[1
]}

Zhang, Jian ^{[1
]}

机构：

[1] Univ Sao Paulo, Inst Matemat & Estat, Caixa Postal 66281, BR-05315970 Sao Paulo, Brazil

来源：

JOURNAL OF ALGEBRA | 2019年 / 530卷

基金：

巴西圣保罗研究基金会;

关键词：

Quantum group; Quantum Weyl algebra; Howe duality; Verma module; Quantum harmonic polynomial; Quantum invariant polynomial; ANALOG; MODULES; ALGEBRA;

D O I：

10.1016/j.jalgebra.2019.04.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct two examples of q-deformed classical Howe dual pairs (sl(2, C), so(3, (C)) and (sl(2, C), sl(n, C)). Moreover, we obtain a noncommutative version of the first fundamental theorem of classical invariant theory. Our approach to these dualities differs from [9] and [11]. Furthermore, we solve the tensor product decomposition problem for Verma modules over U-q(sl(2, C)) provided q is not a root of unity. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：326 / 367

页数：42

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