R-matrix and inverse Shapovalov form

DOI10.1063/1.4950894zbMath1338.81239arXiv1412.3384OpenAlexW258223400MaRDI QIDQ2814203

Andrey Mudrov

Publication date: 20 June 2016

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

Full work available at URL: https://arxiv.org/abs/1412.3384

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) Yang-Baxter equations (16T25)

Related Items (6)

Representations of quantum conjugacy classes of orthosymplectic groups ⋮ Shapovalov elements and Hasse diagrams ⋮ Shapovalov elements of classical and quantum groups ⋮ Quantum exceptional group \(G_2\) and its semisimple conjugacy classes ⋮ Regularization of Mickelsson generators for nonexceptional quantum groups ⋮ Strict quantization of coadjoint orbits

Cites Work

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• Quantum Weyl group and a multiplicative formula for the R-matrix of a simple Lie algebra
• Universal solutions of quantum dynamical Yang-Baxter equations
• The universal \(R\)-matrix for quantum untwisted affine Lie algebras
• Canonical factorization of continuous operator functions relative to the circle
• Invariant *-products on coadjoint orbits and the Shapovalov pairing
• R-matrix and Mickelsson algebras for orthosymplectic quantum groups
• Gelfand–Tsetlin Bases for Classical Lie Algebras
• Operators that Lower or Raise the Irreducible Vector Spaces of U n−1 Contained in an Irreducible Vector Space of Un
• Twisted traces of quantum intertwiners and quantum dynamical \(R\)-matrices corresponding to generalized Belavin-Drinfeld triples.

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