Realization of $U_q({\mathfrak{sp}}_{2n})$ within the Differential Algebra on Quantum Symplectic Space

Symmetry Integrability and Geometry-Methods and Applications

article

Jiao Zhang¹  Naihong Hu² 

[1] Department of Mathematics, Shanghai University, Baoshan Campus;Department of Mathematics, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Minhang Campus

关键词: quantum symplectic group;    quantum symplectic space;    quantum dif ferential operators;    dif ferential calculus;    module algebra;   

DOI  :  10.3842/SIGMA.2017.084

来源: National Academy of Science of Ukraine

【 摘 要 】

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 $U_q({\mathfrak {sp}}_{2n})$.

【 授权许可】

Unknown