|
Realization of $U_q({\mathfrak{sp}}_{2n})$ within the Differential Algebra on Quantum Symplectic Space
Jiao Zhanga, Naihong Hub a Department of Mathematics, Shanghai University, Baoshan Campus, Shangda Road 99, Shanghai 200444, P.R. China
b Department of Mathematics, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Minhang Campus, Dong Chuan Road 500, Shanghai 200241, P.R. China
Abstract:
We realize the Hopf algebra $U_q({\mathfrak {sp}}_{2n})$ as an algebra of quantum differential operators on the quantum symplectic space $\mathcal{X}(f_s;\mathrm{R})$ and prove that $\mathcal{X}(f_s;\mathrm{R})$ is a $U_q({\mathfrak{sp}}_{2n})$-module algebra whose irreducible summands are just its homogeneous subspaces. We give a coherence realization for all the positive root vectors under the actions of Lusztig's braid automorphisms of $U_q({\mathfrak {sp}}_{2n})$.
Keywords:
quantum symplectic group; quantum symplectic space; quantum differential operators; differential calculus; module algebra.
Received: April 18, 2017; in final form October 20, 2017; Published online October 27, 2017
Citation:
Jiao Zhang, Naihong Hu, “Realization of $U_q({\mathfrak{sp}}_{2n})$ within the Differential Algebra on Quantum Symplectic Space”, SIGMA, 13 (2017), 084, 21 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1284 https://www.mathnet.ru/eng/sigma/v13/p84
|
Statistics & downloads: |
Abstract page: | 124 | Full-text PDF : | 30 | References: | 21 |
|