Regularization of Mickelsson generators for nonexceptional quantum groups

Let g′ ⊂ g be a pair of Lie algebras of either symplectic or orthogonal infinitesimal endomorphisms of the complex vector spaces C N −2 ⊂ C N and U q (g′) ⊂ U q (g) be a pair of quantum groups with a triangular decomposition U q (g) = U q (g - ) U q (g + ) U q (h). Let Z q (g, g′) be the correspondi...

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Bibliographic Details
Published in:Theoretical and mathematical physics 2017-08, Vol.192 (2), p.1205-1217
Main Author: Mudrov, A. I.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Generators
Lie groups
Mathematical and Computational Physics
Physics
Physics and Astronomy
Regularization
Theoretical
Trigonometric functions
Vector spaces
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Summary:Let g′ ⊂ g be a pair of Lie algebras of either symplectic or orthogonal infinitesimal endomorphisms of the complex vector spaces C N −2 ⊂ C N and U q (g′) ⊂ U q (g) be a pair of quantum groups with a triangular decomposition U q (g) = U q (g - ) U q (g + ) U q (h). Let Z q (g, g′) be the corresponding step algebra. We assume that its generators are rational trigonometric functions h ∗ → U q (g ± ). We describe their regularization such that the resulting generators do not vanish for any choice of the weight .
ISSN:0040-5779
1573-9333
DOI:10.1134/S0040577917080098