26 citations · 66 across the 26 of their papers we have counts for
27 papers
Billey-Type Formula for KL-Schubert Classes in Hyperbolic Cohomology
Cristian Lenart, Krista Zehr, Changlong Zhong
This paper studies the KL-Schubert classes defined by Kazhdan-Lusztig bases in -theory and hyperbolic cohomology of flag varieties. We first establish Poincaré dualities of thes…
Motivic Chern Classes of Open Projected Richardson Varieties and of Affine Schubert Cells
Changjian Su, Rui Xiong, Changlong Zhong
The open projected Richardson varieties are images of the open Richardson varieties of the complete flag variety under the canonical projection to the partial flag variety. Our mai…
Combinatorial Aspects of Elliptic Schubert Calculus
Cristian Lenart, Rui Xiong, Changlong Zhong
The main goal of this paper is to extend two fundamental combinatorial results in Schubert calculus on flag manifolds from equivariant cohomology and -theory to equivariant elli…
On the formal Peterson subalgebra and its dual
Rui Xiong, Kirill Zainoulline, Changlong Zhong
In the present notes, we study a generalization of the Peterson subalgebra to an oriented (generalized) cohomology theory which we call the formal Peterson subalgebra. Observe that…
A Langlands duality of elliptic Hecke algebras
Gufang Zhao, Changlong Zhong
Associated to any root datum, there is an elliptic affine Hecke algebra defined by Ginzburg, Kapranov, and Vasserot. In this study, we establish a Fourier-Mukai functor from the re…
Elliptic classes via the periodic Hecke module and its Langlands dual
Cristian Lenart, Gufang Zhao, Changlong Zhong
This paper explores a construction of the elliptic classes of the Springer resolution using the periodic Hecke module. The module is established by employing the Poincaré line bund…
Equivariant oriented homology of the affine Grassmannian
Changlong Zhong
We generalize the property of small-torus equivariant K-homology of the affine Grassmannian to general oriented (co)homology theory in the sense of Levine and Morel. The main tool…
Geometric properties of the Kazhdan-Lusztig Schubert basis
Cristian Lenart, Changjian Su, Kirill Zainoulline +1
We study classes determined by the Kazhdan-Lusztig basis of the Hecke algebra in the -theory and hyperbolic cohomology theory of flag varieties. We first show that, in -theor…
The Leray-Hirsch Theorem for equivariant oriented cohomology of flag varieties
J. Matthew Douglass, Changlong Zhong
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 mo…
Structure Constants in equivariant oriented cohomology of flag varieties
Rebecca Goldin, Changlong Zhong
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 cohomol…
On equivariant oriented cohomology of Bott-Samelson varieties
Hao Li, Changlong Zhong
For any Bott-Samelson resolution of the flag variety , and any torus equivariant oriented cohomology , we compute the restriction formu…
Stable bases of the Springer resolution and representation theory
Changjian Su, Changlong Zhong
In this note, we collect basic facts about Maulik and Okounkov's stable bases for the Springer resolution, focusing on their relations to representations of Lie algebras over compl…
Wall-crossings and a categorification of -theory stable bases of the Springer resolution
Changjian Su, Gufang Zhao, Changlong Zhong
We compare the -theory stable bases of the Springer resolution associated to different affine Weyl alcoves. We prove that (up to relabelling) the change of alcoves operators are…
On the K-theory stable bases of the Springer resolution
Changjian Su, Gufang Zhao, Changlong Zhong
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 import…
Formal affine Demazure and Hecke algebras of Kac-Moody root systems
Baptiste Calmès, Kirill Zainoulline, Changlong Zhong
We define the formal affine Demazure algebra and formal affine Hecke algebra associated to a Kac-Moody root system. We prove the structure theorems of these algebras, hence, extend…
Parabolic Kazhdan-Lusztig basis, Schubert classes, and equivariant oriented cohomology
Cristian Lenart, Kirill Zainoulline, Changlong Zhong
We study the equivariant oriented cohomology ring of partial flag varieties using the moment map approach. We define the right Hecke action on this cohomology ring, and…
Representations of the elliptic affine Hecke algebras
Gufang Zhao, Changlong Zhong
We prove that irreducible representations of the elliptic affine Hecke algebras of Ginzburg, Kapranov, and Vasserot are in one-to-one correspondence with certain nilpotent Higgs bu…
Milnor-Witt -groups of local rings
Stefan Gille, Stephen Scully, Changlong Zhong
We introduce Milnor-Witt -groups of local rings and show that the th Milnor-Witt -group of a local ring which contains an infinite field of characteristic not is t…
Equivariant oriented cohomology of flag varieties
Baptiste Calmès, Kirill Zainoulline, Changlong Zhong
Given an equivariant oriented cohomology theory , a split reductive group , a maximal torus in , and a parabolic subgroup containing , we explain how the -eq…
Geometric representations of the formal affine Hecke algebra
Gufang Zhao, Changlong Zhong
For any formal group law, there is a formal affine Hecke algebra defined by Hoffnung, Malagón-López, Savage, and Zainoulline. Coming from this formal group law, there is also an or…
Push-pull operators on the formal affine Demazure algebra and its dual
Baptiste Calmès, Kirill Zainoulline, Changlong Zhong
In the present paper we introduce and study the push pull operators on the formal affine Demazure algebra and its dual. As an application we provide a non-degenerate pairing on the…
On the formal affine Hecke algebra
Changlong Zhong
We study the action of the formal affine Hecke algebra on the formal group algebra, and show that the the formal affine Hecke algebra has a basis indexed by the Weyl group as a mod…
On the γ-filtration of oriented cohomology of complete spin-flags
Changlong Zhong
We study the characteristic map of algebraic oriented cohomology of complete spin-flags and the ideal of invariants of formal group algebra. As an application, we provide an annihi…
A coproduct structure on the formal affine Demazure algebra
Baptiste Calmès, Kirill Zainoulline, Changlong Zhong
In the present paper we generalize the coproduct structure on nil Hecke rings introduced and studied by Kostant-Kumar to the context of an arbitrary algebraic oriented cohomology t…