Vector Bundles on Quantum Conjugacy Classes

Let g be a simple complex Lie algebra of a classical type and U q g the corresponding Drinfeld–Jimbo quantum group at q not a root of unity. With every point t of the fixed maximal torus T of an algebraic group G with Lie algebra g we associate an additive category O q t of U q g -modules that is st...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2024, Vol.284 (1), p.93-125
Main Author: Mudrov, A. I.
Format: Article
Language:English
Subjects:
Algebra
Dimensional stability
Lie groups
Mathematics
Mathematics and Statistics
Modules
Tensors
Toruses
Vectors (mathematics)
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Summary:Let g be a simple complex Lie algebra of a classical type and U q g the corresponding Drinfeld–Jimbo quantum group at q not a root of unity. With every point t of the fixed maximal torus T of an algebraic group G with Lie algebra g we associate an additive category O q t of U q g -modules that is stable under tensor product with finite-dimensional quasiclassical U q g -modules. We prove that O q t is essentially semi-simple and use it to explicitly quantize equivariant vector bundles on the conjugacy class of t .
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-024-07330-7