69 citations · 251 across the 26 of their papers we have counts for
26 papers
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…
Quasimaps to quivers with potentials
Yalong Cao, Gufang Zhao
This paper is concerned with a non-compact GIT quotient of a vector space, in the presence of an abelian group action and an equivariant regular function (potential) on the quotien…
Frobenii on Morava -theoretical quantum groups
Yaping Yang, Gufang Zhao
In this paper, we study a family of new quantum groups labelled by a prime number and a natural number constructed using the Morava -theories. We define the quantum Frob…
Cohomological Hall algebras and perverse coherent sheaves on toric Calabi-Yau 3-folds
Miroslav Rapcak, Yan Soibelman, Yaping Yang +1
We study the Drinfeld double of the (equivariant spherical) Cohomological Hall algebra in the sense of Kontsevich and Soibelman, associated to a smooth toric Calabi-Yau 3-fold .…
Categorification via blocks of modular representations II
Vinoth Nandakumar, Gufang Zhao
Bernstein, Frenkel and Khovanov have constructed a categorification of tensor products of the standard representation of using singular blocks of category $\mathc…
The cohomological Hall algebras of a preprojective algebra with symmetrizer
Yaping Yang, Gufang Zhao
This paper aims at a geometric realization of the Yangian of non-simply laced type in terms of quiver with potentials. For every quiver with symmetrizer, there is an extended quive…
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…
Cohomological Hall algebras, vertex algebras and instantons
Miroslav Rapcak, Yan Soibelman, Yaping Yang +1
We define an action of the (double of) Cohomological Hall algebra of Kontsevich and Soibelman on the cohomology of the moduli space of spiked instantons of Nekrasov. We identify th…
Loop Grassmannians of quivers and affine quantum groups
Ivan Mirkovic, Yaping Yang, Gufang Zhao
We construct for each choice of a quiver , a cohomology theory and a poset a "loop Grassmannian" . This generalizes loop Grassmannians of semisimple…
The PBW theorem for the affine Yangians
Yaping Yang, Gufang Zhao
We prove that the Yangian associated to an untwisted symmetric affine Kac-Moody Lie algebra is isomorphic to the Drinfeld double of a shuffle algebra. The latter is constructed by…
How to sheafify an elliptic quantum group
Yaping Yang, Gufang Zhao
We give an introductory survey of the results in arXiv: 1708.01418. We discuss a sheafified elliptic quantum group associated to any symmetric Kac-Moody Lie algebra. The sheafifica…
Quiver varieties and elliptic quantum groups
Yaping Yang, Gufang Zhao
We define a sheafified elliptic quantum group for any symmetric Kac-Moody Lie algebra. This definition is naturally obtained from the elliptic cohomological Hall algebra of a prepr…
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…
Categorification via blocks of modular representations for sl(n)
Vinoth Nandakumar, Gufang Zhao
Bernstein, Frenkel, and Khovanov have constructed a categorification of tensor products of the standard representation of , where they use singular blocks of categ…
Algebraic elliptic cohomology and flops II: -cobordism
Marc Levine, Yaping Yang, Gufang Zhao
In this paper, we study the algebraic cobordism spectrum in the motivic stable homotopy category of Voevodsky over an arbitrary perfect field . Using the motivic Adams spe…
Cohomological Hall algebras and affine quantum groups
Yaping Yang, Gufang Zhao
We study the preprojective cohomological Hall algebra (CoHA) introduced by the authors in an earlier work for any quiver and any one-parameter formal group . In thi…
On two cohomological Hall algebras
Yaping Yang, Gufang Zhao
We compare two cohomological Hall algebras (CoHA). The first one is the preprojective CoHA introduced by the authors in arXiv:1407.7994 associated to each quiver Q, and each algebr…
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…
The cohomological Hall algebra of a preprojective algebra
Yaping Yang, Gufang Zhao
We introduce for each quiver and each algebraic oriented cohomology theory , the cohomological Hall algebra (CoHA) of , as the -homology of the moduli of representatio…
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…
Real variations of stability conditions for noncommutative symplectic resolutions
Gufang Zhao
A localization theorem for the cyclotomic rational Cherednik algebra over a field of positive characteristic has been proved by Be…
Algebraic elliptic cohomology theory and flops, I
Marc Levine, Yaping Yang, Gufang Zhao
We define the algebraic elliptic cohomology theory coming from Krichever's elliptic genus as an oriented cohomology theory on smooth varieties over an arbitrary perfect field. We s…
Homological finiteness of abelian covers
Alexander I. Suciu, Yaping Yang, Gufang Zhao
We present a method for deciding when a regular abelian cover of a finite CW-complex has finite Betti numbers. To start with, we describe a natural parameter space for all regular…