Realization of U_q(sp_2n) within the Differential Algebra on Quantum Symplectic Space

2016/09/30 by Jiao Zhang, Naihong Hu
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Automorphism #Differential operator #Linear subspace #Mathematics #Pure mathematics #Realization (probability) #Space (punctuation) #Symplectic geometry #Universal enveloping algebra #math.QA #math.RT #math.SG

paper · pdf · doi:10.3842/sigma.2017.084

published in Symmetry Integrability and Geometry Methods and Applications (National Academy of Sciences of Ukraine)

openalex created_date 2016/09/30 · arxiv created 2017/10/27 · openalex publication_date 2017/10/27 · arxiv updated 2017/10/30 · openalex updated_date 2026/08/05

Abstract

We realize the Hopf algebra U q (sp 2n ) as an algebra of quantum differential operators on the quantum symplectic space X (f s ; R) and prove that X (f s ; R) is a U q (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 (sp 2n ).

Citations

• Representation Theory
• Quantum Divided Power Algebra, Q-Derivatives, and Some New Quantum Groups
• Differential calculus on compact matrix pseudogroups (quantum groups)
• Loewy filtration and quantum de Rham cohomology over quantum divided power algebra
• Hopf Modules and Yetter - Drinfel′d Modules
• Quantum groups and representations of monoidal categories
• The Green rings of the 2-rank Taft algebra and its two relatives twisted
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• Quantization of Lie Groups and Lie Algebras
• Quantum Groups