50 citations · 222 across the 52 of their papers we have counts for
21 papers · 1 filter
Tao-Travkin equivalence revisited
Penghui Li, David Nadler, Yakov Varshavsky +1
We give a simpler proof of the theorem of J.~Tao and R.~Travkin saying that (the neutral block of) the affine Hecke category is the monoidal colimit of finite Hecke categories. The…
Perverse filtration on the cohomology of affine Springer fibers
Zhiwei Yun
We show that the top cohomology of any affine Springer fiber, as a Weyl group representation, contains a large part of the total cohomology of certain Springer fibers. The main ing…
Character sheaves on loop Lie algebras: polar partition
Ngo Bao Chau, Zhiwei Yun
In this paper we propose a partition of loop Lie algebras into invariant sets parametrized by polar data. Our polar partition is motivated by J-K. Yu's construction of supercuspida…
Functions on the commuting stack via Langlands duality
Penghui Li, David Nadler, Zhiwei Yun
We calculate the dg algebra of global functions on commuting stacks of complex reductive groups using tools from Betti Geometric Langlands. In particular, we prove that the ring of…
Minimal reduction type and the Kazhdan-Lusztig map
Zhiwei Yun
We introduce the notion of minimal reduction type of an affine Springer fiber, and use it to define a map from the set of conjugacy classes in the Weyl group to the set of nilpoten…
From conjugacy classes in the Weyl group to representations
George Lusztig, Zhiwei Yun
We define a map from the set of conjugacy classes of a Weyl group W to the representation ring of W tensored with the ring of polynomials in one variable.
Semilinear automorphisms of classical groups and quivers
Jinwei Yang, Zhiwei Yun
For a classical group over a field together with a finite-order automorphism that acts compatibly on , we describe the fixed point subgroup of on and the eig…
Higher signs for Coxeter groups
Zhiwei Yun
We define and study cocycles on a Coxeter group in each degree generalizing the sign function. When the Coxeter group is a Weyl group, we explain how the degree three cocycle arise…
Endoscopy for Hecke categories, character sheaves and representations
George Lusztig, Zhiwei Yun
For a split reductive group over a finite field, we show that the neutral block of its mixed Hecke category with a fixed monodromy under the torus action is monoidally equivale…
Hitchin type moduli stacks in automorphic representation theory
Zhiwei Yun
In the study of automorphic representations over a function field, Hitchin moduli stack and its variants naturally appear and their geometry helps the comparison of trace formulae.…
Z/m-graded Lie algebras and perverse sheaves, IV
George Lusztig, Zhiwei Yun
Let G be a reductive group over C. Assume that the Lie algebra g of G has a given grading (g_j) indexed by a cyclic group Z/m such that g_0 contains a Cartan subalgebra of g. The s…
Geometric Langlands correspondence for SL(2), PGL(2) over the pair of pants
David Nadler, Zhiwei Yun
We establish the Geometric Langlands correspondence for rank one groups over the projective line with three points of tame ramification.
-graded Lie algebras and perverse sheaves, III: graded double affine Hecke algebra
George Lusztig, Zhiwei Yun
In this paper we construct representations of certain graded double affine Hecke algebras (DAHA) with possibly unequal parameters from geometry. More precisely, starting with a sim…
-graded Lie algebras and perverse sheaves, II
George Lusztig, Zhiwei Yun
We consider a fixed block for the equivariant perverse sheaves with nilpotent support in the -graded ccomponent of a semisimple cyclically graded Lie algebra. We give a combinat…
Lectures on Springer theories and orbital integrals
Zhiwei Yun
These are the expanded lecture notes from the author's mini-course during the graduate summer school of the Park City Math Institute in 2015. The main topics covered are: geometry…
Z/m-graded Lie algebras and perverse sheaves, I
George Lusztig, Zhiwei Yun
We give a block decomposition of the equivariant derived category arising from a cyclically graded Lie algebra. This generalizes certain aspects of the generalized Springer corresp…
Geometric representations of graded and rational Cherednik algebras
Alexei Oblomkov, Zhiwei Yun
We provide geometric constructions of modules over the graded Cherednik algebra and the rational Cherednik algebra attached to a simple…
A -analogue of weight multiplicities
George Lusztig, Zhiwei Yun
We prove a conjecture in \cite{L} stating that certain polynomials introduced in \cite{LV1} for twisted involutions in an affine Weyl group give -analogues of…
The spherical part of the local and global Springer actions
Zhiwei Yun
The affine Weyl group acts on the cohomology (with compact support) of affine Springer fibers (local Springer theory) and of parabolic Hitchin fibers (global Springer theory). In t…
On Koszul duality for Kac-Moody groups
Roman Bezrukavnikov, Zhiwei Yun
For any Kac-Moody group with Borel , we give a monoidal equivalence between the derived category of -equivariant mixed complexes on the flag variety and (a certain…
Integral homology of loop groups via Langlands dual groups
Zhiwei Yun, Xinwen Zhu
Let K be a connected compact Lie group, and G be its complexification. The homology of the based loop group ΩK with integer coefficients is naturally a \ZZ-Hopf algebra. After poss…