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
Published electronically:
September 8, 2011
MathSciNet review:
2833470
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Abstract: We generalize Chevalley's theorem about restriction to the case when a semisimple Lie algebra is replaced by a quantum group and the target space of the polynomial maps is replaced by a finite dimensional representation of this quantum group. We prove that the restriction map is injective and describe the image.
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Bibliography
[Br] A. Broer, The sum of generalized exponents and Chevalley's restriction theorem for modules of covariants , Indag. Math. (N.S.) 6 (1995), no. 4, 385-396. MR 1365182 (96j:20058)
[Bo] A. Borel, Linear algebraic groups , Second edition. Graduate Texts in Mathematics, 126. Springer-Verlag, New York, 1991. MR 1102012 (92d:20001)
[EV1] P. Etingof, A. Varchenko, Dynamical Weyl groups and applications , Adv. Math. 167 (2002), no. 1, 74-127. MR 1901247 (2003d:17004)
[EV2] P. Etingof, A. Varchenko, Traces of intertwiners for quantum groups and difference equations, I , Duke Math. J. 104 (2000), no. 3, 391-432. MR 1781477 (2001k:17021)
[EFK] P. Etingof, I. Frenkel, A. Kirillov Jr, Spherical functions on affine Lie groups , Duke Math. J. 80 (1995), no. 1, 59-90. MR 1360611 (97e:22018)
[KNV] S. Khoroshkin, M. Nazarov, E. Vinberg, A generalized Harish-Chandra isomorphism , Adv. Math. 226 (2011), no. 2, 1168-1180. MR 2737780
[KS] L. Korogodski, Y. Soibelman, Algebras of Functions on Quantum Groups: Part I , Mathematical Surveys and Monographs, 56. American Mathematical Society, Providence, RI, 1998. MR 1614943 (99a:17022)
[T] T. Tanisaki, Harish-Chandra isomorphisms for quantum algebras , Comm. Math. Phys. 127 (1990), no. 3, 555-571. MR 1040894 (92e:17022)
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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:
http://dx.doi.org/10.1090/S1088-4165-2011-00408-8
PII:
S 1088-4165(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.