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Chevalley restriction theorem for vector-valued functions on quantum groups


Author: Martina Balagović
Journal: Represent. Theory 15 (2011), 617-645
MSC (2010): Primary 17B37, 20G42
DOI: https://doi.org/10.1090/S1088-4165-2011-00408-8
Published electronically: September 8, 2011
MathSciNet review: 2833470
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Abstract: We generalize Chevalley's theorem about restriction $ \operatorname{Res}: \mathbb{C}[\mathfrak{g}]^{\mathfrak{g}} \to \mathbb{C}[\mathfrak{h}]^W$ to the case when a semisimple Lie algebra $ \mathfrak{g}$ is replaced by a quantum group and the target space $ \mathbb{C}$ of the polynomial maps is replaced by a finite dimensional representation $ V$ of this quantum group. We prove that the restriction map $ \operatorname{Res}:(O_{q}(G)\otimes V)^{U_{q}(\mathfrak{g})}\to O(H)\otimes V$ is injective and describe the image.


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Additional Information

Martina Balagović
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email: martinab@math.mit.edu

DOI: https://doi.org/10.1090/S1088-4165-2011-00408-8
Received by editor(s): April 2, 2010
Received by editor(s) in revised form: June 10, 2011
Published electronically: September 8, 2011
Additional Notes: This work was partially supported by the NSF grant DMS-0504847.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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