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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Chevalley restriction theorem for vector-valued functions on quantum groups
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by Martina Balagović PDF
Represent. Theory 15 (2011), 617-645 Request permission


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
  • MR Author ID: 919905
  • Email:
  • 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.
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 15 (2011), 617-645
  • MSC (2010): Primary 17B37, 20G42
  • DOI:
  • MathSciNet review: 2833470