A Schubert basis in equivariant elliptic cohomology

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.

arXiv admin note: text overlap with arXiv:1408.5952

References in corpus (5)

• Formal Hecke algebras and algebraic oriented cohomology theories
• A coproduct structure on the formal affine Demazure algebra
• Generalized Schubert Calculus
• Elliptic formal group laws, integral Hirzebruch genera and Krichever genera
• Towards generalized cohomology Schubert calculus via formal root polynomials

Cited by in corpus (2)

• Elliptic classes of Schubert varieties via Bott-Samelson resolution
• Equivariant motives and geometric representation theory. (with an appendix by F. Hörmann and M. Wendt)