Realization of Uq(sp₂n) within the Differential Algebra on Quantum Symplectic Space

Abstract

We realize the Hopf algebra Uq(sp₂n) as an algebra of quantum differential operators on the quantum symplectic space X(fs;R) and prove that X(fs;R) is a Uq(sp₂n)-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 Uq(sp₂n).