New York Journal of Mathematics
Volume 23 (2017) 711-737


Cristian Lenart and Kirill Zainoulline

A Schubert basis in equivariant elliptic cohomology

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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

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.


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).

Author information

Cristian Lenart:
Department of Mathematics and Statistics, State University of New York at Albany, Albany, NY 12222, U.S.A.

Kirill Zainoulline:
Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Street, Ottawa, ON, K1N 6N5, Canada