Посилання:Realization of Uq(sp₂n) within the Differential Algebra on Quantum Symplectic Space / J. Zhang, N. Hu // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 25 назв. — англ.
Підтримка:The authors would appreciate the referees for their useful comments and good suggestions for
improving the paper. The first author is supported by the NSFC (Grants No. 11101258 and
No. 11371238). The second author is supported by the NSFC (Grant No. 11771142).
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).