Generalized Schubert Calculus

Abstract

In this paper we study the T-equivariant generalized cohomology of flag varieties using two models, the Borel model and the moment graph model. We study the differences between the Schubert classes and the Bott-Samelson classes. After setup of the general framework we compute, for classes of Schubert varieties of complex dimension <4 in rank 2 (including A_2, B_2, G_2 and A_1^{(1)}), moment graph representatives, Pieri-Chevalley formulas and products of Schubert classes. These computations generalize the computations in equivariant K-theory for rank 2 cases which are given in Griffeth-Ram arXiv:math/0405333.

References in corpus (4)

• The elliptic Weyl character formula
• Formal Hecke algebras and algebraic oriented cohomology theories
• Richardson Varieties Have Kawamata Log Terminal Singularities
• Schubert varieties are log Fano over the integers

Cited by in corpus (8)

• A coproduct structure on the formal affine Demazure algebra
• On Some Quadratic Algebras I $\frac{1}{2}$: Combinatorics of Dunkl and Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and Reduced Polynomials
• K-theoretic crystals for set-valued tableaux of rectangular shapes
• A Schubert basis in equivariant elliptic cohomology
• A model for complex analytic equivariant elliptic cohomology from quantum field theory
• Asymmetric function theory
• Push-pull operators on the formal affine Demazure algebra and its dual
• Generalized (co)homology of the loop spaces of classical groups and the universal factorial Schur $P$- and $Q$-functions