Related papers: Notes on the arithmetic of Hecke L-functions

In this paper we investigate arithmetic properties of automorphic forms on the group G' = GL_m/D, for a central division-algebra D over an arbitrary number field F. The results of this article are generalizations of results in the split…

We extend the computations in [AGM1, AGM2, AGM3] to find the cohomology in degree five of a congruence subgroup Gamma of SL(4,Z) with coefficients in a field K, twisted by a nebentype character eta, along with the action of the Hecke…

A $GL_d$-pseudocharacter is a function from a group $\Gamma$ to a ring $k$ satisfying polynomial relations which make it "look like" the character of a representation. When $k$ is an algebraically closed field, Taylor proved that…

In this paper we study homological properties of modules over an affine Hecke algebra H. In particular we prove a comparison result for higher extensions of tempered modules when passing to the Schwartz algebra S, a certain topological…

We study the action of the derived Hecke algebra in the setting of dihedral weight one forms, and prove a conjecture of the second- and fourth- named authors relating this action to certain Stark units associated to the symmetric square…

In this paper, we compute the Hecke action of a certain test function on the space of an unramified principal series of a connected reductive group over a non-archimedean local field by using the theory of Iwahori--Hecke algebra. As an…

This paper computes the irreducible characters of the alternating Hecke algebras, which are deformations of the group algebras of the alternating groups. More precisely, we compute the values of the irreducible characters of the semisimple…

We prove that Hecke eigenvalues for any Hilbert and Siegel modular forms are algebraic integers. Our method does not rely on cohomologicality nor Galois representations. We apply the integrality of Hecke eigenvalues for Hilbert modular…

We give a construction of an affine Hecke algebra associated to any Coxeter group acting on an abelian variety by reflections; in the case of an affine Weyl group, the result is an elliptic analogue of the usual double affine Hecke algebra.…

Let $\pi$ be an irreducible cuspidal automorphic generic representation of $\mathrm{Sp}_{2n}(\mathbb{A})$ and let $\chi:F^\times\backslash \mathbb{A}^\times\to \mathbb{C}^\times$ be a unitary idele class character. In this note, we present…

We introduce a new collection of partially global Galois cohomology classes subsuming both plectic Heegner points and mock plectic invariants. The former are recovered as localizations of plectic Heegner classes, while the latter arise as…

We determine the action of the Hecke operators \(T_{\mathfrak{p},i}\) on the coefficient forms \(g_{1}, \dots, g_{r-1}, g_{r} = \Delta\), and \(h\), which together generate the ring of modular forms for \(\mathrm{GL}(r,…

For certain algebraic Hecke characters chi of an imaginary quadratic field F we define an Eisenstein ideal in a p-adic Hecke algebra acting on cuspidal automorphic forms of GL_2/F. By finding congruences between Eisenstein cohomology…

We relate non-critical special values $p$-adic $L$-functions associated to algebraic Hecke characters of an imaginary quadratic number field with class number one to $p$-adic Coleman function called the $p$-adic Eisenstein-Kronecker series,…

Let G be a complex symplectic group. We introduce a G x (C ^x) ^{l + 1}-variety N_{l}, which we call the l-exotic nilpotent cone. Then, we realize the Hecke algebra H of type C_n ^(1) with three parameters via equivariant algebraic K-theory…

We classify gradings on the Hecke category that refine the standard integer grading. We also classify object-preserving autoequivalences of the Hecke category. We obtain a natural bigrading on the Hecke category which is related to the…

We explain how to compute idempotents that correspond to the indecomposable objects in the Hecke category. Closed formulas are provided for some common coefficients that appear in these idempotents. We also explain how to compute…

We introduce graded Hecke algebras H based on a (possibly disconnected) complex reductive group G and a cuspidal local system L on a unipotent orbit of a Levi subgroup M of G. These generalize the graded Hecke algebras defined and…

The Hecke algebra H(G,H) of a Hecke pair (G,H) is studied using the Schlichting completion (G',H'), which is a Hecke pair whose Hecke algebra is isomorphic to H(G,H) and which is topologized so that H' is a compact open subgroup of G'. In…

In this paper, we look at the problem of determining the composition factors for the affine graded Hecke algebra via the computation of Kazhdan-Lusztig type polynomials. We review the algorithms of \cite{L1,L2}, and use them in particular…