• Corpus ID: 221534688

Structure Constants in equivariant oriented cohomology of flag varieties

@article{Goldin2020StructureCI,
  title={Structure Constants in equivariant oriented cohomology of flag varieties},
  author={Rebecca F. Goldin and Changlong Zhong},
  journal={arXiv: Algebraic Geometry},
  year={2020}
}
We obtain a formula for structure constants of certain variant form of Bott-Samelson classes for equivariant oriented cohomology of flag varieties. Specializing to singular cohomology/K-theory, we recover formulas of structure constants of Schubert classes of Goldin-Knutson, and that of structure constants of Segre-Schwartz-MacPherson classes of Su. We also obtain a formula for K-theoretic stable basis. Our method comes from the study of formal affine Demazure algebra, so is purely algebraic… 
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A G ] 7 J an 2 02 2 THE LERAY-HIRSCH THEOREM FOR ORIENTED COHOMOLOGY OF FLAG VARIETIES

We construct two explicit Leray-Hirsch isomorphisms for torus equivariant oriented cohomology of flag varieties and give several applications. One isomorphism is geometric, based on Bott-Samelson…

On equivariant oriented cohomology of Bott-Samelson varieties

For any Bott-Samelson resolution $q_{I}:\hat{X_{I}}\rightarrow G/B$ of the flag variety $G/B$, and any torus equivariant oriented cohomology $h_T$, we compute the restriction formula of certain basis…

The Leray-Hirsch Theorem for equivariant oriented cohomology of flag varieties

We use the formal affine Demazure algebra to construct an explicit Leray-Hirsch Theorem for torus equivariant oriented cohomology of flag varieties. We then generalize the Borel model of such theory…

References

SHOWING 1-10 OF 26 REFERENCES

Structure constants for Chern classes of Schubert cells

  • C. Su
  • Mathematics
    Mathematische Zeitschrift
  • 2020
A formula for the structure constants of the multiplication of Schubert classes is obtained in (Rebecca and Allen. arXiv preprint arXiv:1909.05283, 2019). In this note, we prove analogous formulae…

On the K-theory stable bases of the Springer resolution

Cohomological and K-theoretic stable bases originated from the study of quantum cohomology and quantum K-theory. Restriction formula for cohomological stable bases played an important role in…

Invariants, torsion indices and oriented cohomology of complete flags

In the present notes we generalize the classical work of Demazure [Invariants sym\'etriques entiers des groupes de Weyl et torsion] to arbitrary oriented cohomology theories and formal group laws.…

A coproduct structure on the formal affine Demazure algebra

In the present paper, we generalize the coproduct structure on nil Hecke rings introduced and studied by Kostant and Kumar to the context of an arbitrary algebraic oriented cohomology theory and its…

Algebraic Cobordism

Together with F. Morel, we have constructed in [6, 7, 8] a theory of algebraic cobordism, an algebro-geometric version of the topological theory of complex cobordism. In this paper, we give a survey…

Shadows of characteristic cycles, Verma modules, and positivity of Chern-Schwartz-MacPherson classes of Schubert cells

Chern-Schwartz-MacPherson (CSM) classes generalize to singular and/or noncompact varieties the classical total homology Chern class of the tangent bundle of a smooth compact complex manifold. The…

Equivariant oriented cohomology of flag varieties

Given an equivariant oriented cohomology theory $h$, a split reductive group $G$, a maximal torus $T$ in $G$, and a parabolic subgroup $P$ containing $T$, we explain how the $T$-equivariant oriented…

T-equivariant K-theory of generalized flag varieties

Abstract Let G be a Kac—Moody group with Borel subgroup B and compact maximal torus T. Analogous to Kostant and Kumar [Kostant, B. & Kumar, S. (1986) Proc. Natl. Acad. Sci. USA 83, 1543-1545], we…

Formal Hecke algebras and algebraic oriented cohomology theories

In the present paper, we generalize the construction of the nil Hecke ring of Kostant–Kumar to the context of an arbitrary formal group law, in particular, to an arbitrary algebraic oriented…

T-equivariant K-theory of generalized flag varieties.

Many of the results of this paper are new in the finite case (i.e., G is a finite-dimensional semisimple group over C) as well.