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Realization of $U_q({\mathfrak{sp}}_{2n})$ within the Differential Algebra on Quantum Symplectic Space
Symmetry, integrability and geometry: methods and applications, Tome 13 (2017) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {Jiao Zhang and Naihong Hu},
     title = {Realization of $U_q({\mathfrak{sp}}_{2n})$ within the {Differential} {Algebra} on {Quantum} {Symplectic} {Space}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a83/}
}
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Jiao Zhang; Naihong Hu. Realization of $U_q({\mathfrak{sp}}_{2n})$ within the Differential Algebra on Quantum Symplectic Space. Symmetry, integrability and geometry: methods and applications, Tome 13 (2017). http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a83/

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