Quantum Howe duality and invariant polynomials
Quantum Algebra
2018-11-28 v2
Abstract
We construct two examples of q-deformed classical Howe dual pairs (sl(2,C), sl(2,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 duality differs from the paper of Lehrer-Zhang-Zhang. 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.
Cite
@article{arxiv.1712.03006,
title = {Quantum Howe duality and invariant polynomials},
author = {Vyacheslav Futorny and Libor Krizka and Jian Zhang},
journal= {arXiv preprint arXiv:1712.03006},
year = {2018}
}