相关论文: Mod-$2$ Hecke algebras of level $3$ and $5$
An affine Hecke algebra H contains a large abelian subalgebra A. The center Z of H is the subalgebra of Weyl group invariant elements in A. The natural trace of the affine Hecke algebra can be written as an integral of a rational $n$ form…
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 algebra by a version of the Hall…
We consider quantum symmetric algebras, FRT bialgebras and, more generally, intertwining algebras for pairs of Hecke symmetries which represent quantum hom-spaces. The paper makes an attempt to investigate Koszulness and Gorensteinness of…
Graded Hecke algebras can be constructed geometrically, with constructible sheaves and equivariant cohomology. The input consists of a complex reductive group G (possibly disconnected) and a cuspidal local system on a nilpotent orbit for a…
We study double affine Hecke algebras at roots of unity and their relations with deformed Hilbert schemes.
This paper is devoted to deformation theory of graded Lie algebras over $\Z$ or $\Z_l$ with finite dimensional graded pieces. Such deformation problems naturally appear in number theory. In the first part of the paper, we use Schlessinger…
A description is given of all primitive differential series mod p of order 1 which are eigenvectors of all the Hecke operators and which are differential Fourier expansions of differential modular forms of arbitrary order and given weight;…
We study the representation theory of graded Hecke algebras, starting from scratch and focusing on representations that are obtained with induction from a discrete series representation of a parabolic subalgebra. We determine all…
We study the algebraic properties of the five-parameter family $H(t_1,t_2,t_3,t_4;q)$ of double affine Hecke algebras of type $C^\vee C_1$. This family generalizes Cherednik's double affine Hecke algebras of rank 1. It was introduced by…
We investigate some key analytic properties of Fourier coefficients and Hecke eigenvalues attached to scalar-valued Siegel cusp forms $F$ of degree 2, weight $k$ and level $N$. First, assuming that $F$ is a Hecke eigenform that is not of…
We introduce a derived enhancement of local Galois deformation rings that we call the "spectral Hecke algebra", in analogy to a construction in the Geometric Langlands program. This is a Hecke algebra that acts on the spectral side of the…
A family of deformed Hopf algebras corresponding to the classical maximal isometry algebras of zero-curvature N-dimensional spaces (the inhomogeneous algebras iso(p,q), p+q=N, as well as some of their contractions) are shown to have a…
In the present article we define the algebra of differential modular forms and we prove that it is generated by Eisenstein series of weight $2,4$ and 6. We define Hecke operators on them, find some analytic relations between these…
The main result of the paper is the classification of all (nonassociative) algebras of level two, i.e. such algebras that maximal chains of nontrivial degenerations starting at them have length two. During this classification we obtain an…
This is a survey paper about representation theory and noncommutative geometry of reductive p-adic groups G. The main focus points are: 1. The structure of the Hecke algebra H(G), the Harish-Chandra-Schwartz algebra S(G) and the reduced…
We construct a new family of irreducible modules over any basic classical affine Kac-Moody Lie superalgebra which are induced from modules over the Heisenberg subalgebra. We also obtain irreducible deformations of these modules for the…
We present a deformation theory associated to the higher Hochschild cohomology $H_{S^2}^*(A,A)$. We also study a $G$-algebra structure associated to this deformation theory.
We geometrize the mod $p$ Satake isomorphism of Herzig and Henniart-Vign\'eras using Witt vector affine flag varieties for reductive groups in mixed characteristic. We deduce this as a special case of a formula, stated in terms of the…
Recently Delorme and Opdam have generalized the theory of R-groups towards affine Hecke algebras with unequal labels. We apply their results in the case where the affine Hecke algebra is of type B, for an induced discrete series…
We give a new, simple proof of the trace formula for Hecke operators on modular forms for finite index subgroups of the modular group. The proof uses algebraic properties of certain universal Hecke operators acting on period polynomials of…