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

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

References in corpus (3)

• The Green rings of the 2-rank Taft algebra and its two relatives twisted
• Double-bosonization and Majid's conjecture, (I): rank-induction of $ABCD$
• Loewy filtration and quantum de Rham cohomology over quantum divided power algebra