R-matrix and Mickelsson algebras for orthosymplectic quantum groups

DOI10.1063/1.4927582zbMath1322.81055arXiv1410.6493OpenAlexW3099915244MaRDI QIDQ2943423

Andrey Mudrov, Thomas Ashton

Publication date: 11 September 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.6493

zbMATH Keywords

R-matrixMickelsson algebra

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Applications of Lie groups to the sciences; explicit representations (22E70) Finite-dimensional groups and algebras motivated by physics and their representations (81R05)

Related Items (5)

Representations of quantum conjugacy classes of orthosymplectic groups ⋮ Shapovalov elements and Hasse diagrams ⋮ Regularization of Mickelsson generators for nonexceptional quantum groups ⋮ Diagonal reduction algebra for $\mathfrak{osp}(1|2)$ ⋮ R-matrix and inverse Shapovalov form

Cites Work

• On representations of quantum conjugacy classes of \(\mathrm{GL}(n)\)
• \(q\)-analog of Gelfand-Graev basis for the noncompact quantum algebra \(U_q(u(n,1))\)
• Step algebras of semi-simple subalgebras of Lie algebras
• Projection operators for simple Lie groups. II: General scheme for constructing lowering operators. The groups \(\mathrm{SU}(n)\)
• Mickelsson algebras and Zhelobenko operators.
• Gelfand–Tsetlin Bases for Classical Lie Algebras
• Step algebras of quantum algebras of typeA,BandD
• Operators that Lower or Raise the Irreducible Vector Spaces of U n−1 Contained in an Irreducible Vector Space of Un
• Projection operators for simple lie groups
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