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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A classification of $ H$-primes of quantum partial flag varieties


Author: Milen Yakimov
Journal: Proc. Amer. Math. Soc. 138 (2010), 1249-1261
MSC (2010): Primary 16W50; Secondary 20G42, 14M15
Published electronically: December 2, 2009
MathSciNet review: 2578519
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Abstract: We classify the invariant prime ideals of a quantum partial flag variety under the action of the related maximal torus. As a result we construct a bijection between them and the torus orbits of symplectic leaves of the standard Poisson structure on the corresponding flag variety. It was previously shown by K. Goodearl and the author that the latter are precisely the Lusztig strata of the partial flag variety.


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Additional Information

Milen Yakimov
Affiliation: Department of Mathematics, Louisiana State Univerity, Baton Rouge, Louisiana 70803 – and – Department of Mathematics, University of California, Santa Barbara, California 93106
Email: yakimov@math.lsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10180-6
PII: S 0002-9939(09)10180-6
Keywords: Quantum partial flag varieties, prime ideals, Lusztig's stratification
Received by editor(s): May 31, 2009
Received by editor(s) in revised form: August 11, 2009, and August 27, 2009
Published electronically: December 2, 2009
Communicated by: Gail R. Letzter
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.