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Cristian Lenart and Kirill Zainoulline
A Schubert basis in equivariant elliptic cohomology view print
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| Published: |
June 15, 2017 |
| Keywords: |
Schubert calculus, elliptic cohomology, flag variety, Hecke algebra, Kazhdan-Lusztig basis |
| Subject: |
14M15, 14F43, 55N20, 55N22, 19L47, 05E99 |
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Abstract
We address the problem of defining Schubert classes independently of a reduced word in equivariant elliptic cohomology, based on the Kazhdan-Lusztig basis of a corresponding Hecke algebra. We study some basic properties of these classes, and make two important conjectures about them: a positivity conjecture, and the agreement with the topologically defined Schubert classes in the smooth case. We prove some special cases of these conjectures.
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| Acknowledgements
C.L. was partially supported by the NSF grant DMS-1362627. K.Z. was partially supported by the NSERC Discovery grant 385795-2010 and the Early Researcher Award (Ontario).
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| Author information
Cristian Lenart:
Department of Mathematics and Statistics, State University of New York at Albany, Albany, NY 12222, U.S.A.
clenart@albany.edu
Kirill Zainoulline:
Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Street, Ottawa, ON, K1N 6N5, Canada
kirill@uottawa.ca
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