The Trace of the affine Hecke category
@inproceedings{Gorsky2022TheTO, title={The Trace of the affine Hecke category}, author={Eugene Gorsky and Andrei Neguct}, year={2022} }
We compare the (horizontal) trace of the affine Hecke category with the elliptic Hall algebra, thus obtaining an “affine” version of the construction of [14]. Explicitly, we show that the aforementioned trace is generated by the objects Ed = Tr(Y d1 1 . . . Y dn n T1 . . . Tn−1) as d = (d1, . . . , dn) ∈ Z , where Yi denote the Wakimoto objects of [9] and Ti denote Rouquier complexes. We compute certain categorical commutators between the Ed’s and show that they match the categorical…
References
SHOWING 1-10 OF 44 REFERENCES
On the Hall algebra of an elliptic curve, I
- Mathematics
- 2005
This paper is a sequel to math.AG/0505148, where the Hall algebra U^+_E of the category of coherent sheaves on an elliptic curve E defined over a finite field was explicitly described, and shown to…
The elliptic Hall algebra and the deformed Khovanov Heisenberg category
- MathematicsSelecta Mathematica
- 2018
We give an explicit description of the trace, or Hochschild homology, of the quantum Heisenberg category defined in Licata and Savage (Quantum Topol 4(2):125–185, 2013. arXiv:1009.3295). We also…
The cohomological Hall algebra of a surface and factorization cohomology
- Mathematics
- 2019
For a smooth quasi-projective surface S over complex numbers we consider the Borel-Moore homology of the stack of coherent sheaves on S with compact support and make this space into an associative…
Flag Hilbert schemes, colored projectors and Khovanov-Rozansky homology
- MathematicsAdvances in Mathematics
- 2021
On two geometric realizations of an affine Hecke algebra
- Mathematics
- 2012
The article is a contribution to the local theory of geometric Langlands duality. The main result is a categorification of the isomorphism between the (extended) affine Hecke algebra associated to a…
Drinfeld realization of the elliptic Hall algebra
- Mathematics
- 2010
We give a new presentation of the Drinfeld double $\boldsymbol{\mathcal {E}}$ of the (spherical) elliptic Hall algebra $\boldsymbol{\mathcal{E}}^{+}$ introduced in our previous work (Burban and…
Equivariant K-theory of Hilbert schemes via shuffle algebra
- Mathematics
- 2011
In this paper we construct the action of Ding-Iohara and shuffle algebras in the sum of localized equivariant K-groups of Hilbert schemes of points on C^2. We show that commutative elements K_i of…
A commutative algebra on degenerate CP^1 and Macdonald polynomials
- Mathematics
- 2009
We introduce a unital associative algebra A over degenerate CP^1. We show that A is a commutative algebra and whose Poincar'e series is given by the number of partitions. Thereby we can regard A as a…
Affine braid group actions on derived categories of Springer resolutions
- Mathematics
- 2011
In this paper we construct and study an action of the affine braid group associated to a semi-simple algebraic group on derived categories of coherent sheaves on various varieties related to the…
A Categorical Quantum Toroidal Action on Hilbert Schemes
- Mathematics
- 2020
We categorify the commutation of Nakajima's Heisenberg operators $P_{\pm 1}$ and their infinitely many counterparts in the quantum toroidal algebra $U_{q_1,q_2}(\ddot{gl_1})$ acting on the…