Quantum Howe duality and invariant polynomials

Author(s)

Futorny, Vyacheslav ^[1] ; Krizka, Libor ^[1] ; Zhang, Jian ^[1]

Affiliation

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

• Document type: Journal article
• Source: Journal of Algebra; v. 530, p. 326-367, JUL 15 2019.
• Web of Science Citations: 0

Abstract

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. (AU)

• FAPESP's process: 15/05927-0 - Quantum determinants and categorification of quantum groups
• Grantee: Jian Zhang
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 14/09310-5 - Algebraic structures and their representations
• Grantee: Vyacheslav Futorny
• Support Opportunities: Research Projects - Thematic Grants