Related papers: Character values and Hochschild homology

For a locally compact, totally disconnected group $G$, a subgroup $H$ and a character $\chi:H \to \mathbb{C}^{\times}$ we define a Hecke algebra $\mathcal{H}_\chi$ and explore the connection between commutativity of $\mathcal{H}_\chi$ and…

Let G be an almost simple, simply connected algebraic group over an algebraically closed field of characteristic p>0. In this paper we restate our conjecture from 1979 on the characters of irreducible modular representations of G so that it…

Let G be a reductive group over a non-archimedean local field F. Consider an arbitrary Bernstein block Rep(G)^s in the category of complex smooth G-representations. In earlier work the author showed that there exists an affine Hecke algebra…

We show there is a class of symplectic Lie algebra representations over any field of characteristic not 2 or 3 that have many of the exceptional algebraic and geometric properties of both symmetric three forms in two dimensions and…

For a reductive group G and a finite order Cartan-type automorphism \iota of G, we construct an eigenvariety parameterizing \iota-invariant cuspidal Hecke eigensystems of G. In particular, for G = Gln, we prove, any self-dual cuspidal Hecke…

We introduce an elliptic version of the Grothendieck-Springer sheaf and establish elliptic analogues of the basic results of Springer theory. From a geometric perspective, our constructions specialize geometric Eisenstein series to the…

In this paper, we will show that for a smooth quasi-projective variety over $\C,$ and a regular function $W:X\to \C,$ the periodic cyclic homology of the DG category of matrix factorizations $MF(X,W)$ is identified (unde Riemann-Hilbert…

We revisit Haiman's conjecture on the relations between characters of Kazdhan-Lusztig basis elements of the Hecke algebra over the symmetric group. The conjecture asserts that, for purposes of character evaluation, any Kazhdan-Lusztig basis…

In Part 1 we study the spherical functions on compact symmetric pairs of arbitrary rank under a suitable multiplicity freeness assumption and additional conditions on the branching rules. The spherical functions are taking values in the…

Let $\mathcal C$ be category over a commutative ring $k$, its Hochschild-Mitchell homology and cohomology are denoted respectively $HH_*(\mathcal C)$ and $HH^*(\mathcal C).$ Let $G$ be a group acting on $\mathcal C$, and $\mathcal C[G]$ be…

Let n be a positive integer, F be a non-Archimedean locally compact field of odd residue characteristic p and G be an inner form of GL(2n,F). This is a group of the form GL(r,D) for a positive integer r and division F-algebra D of reduced…

We propose a definition of characters in the context of Schneider-Teitelbaum's theory of locally analytic representations of p-adic reductive groups. This character will be a function on a compact subgroup of a maximal torus of the…

The main purpose of this article is to give the integral cohomology of classical principal congruence subgroups in SL(2,Z) as well as their analogues in the third braid group with local coefficients in symmetric powers of the natural…

We classify and explicitly construct the irreducible graded representations of anti-spherical Hecke categories which are concentrated in one degree. Each of these homogeneous representations is one-dimensional and can be cohomologically…

The character formulas of Sally and Shalika are an early triumph in $p$-adic harmonic analysis, but, to date, the calculations underlying the formulas have not been available. In this paper, which should be viewed as a precursor of the…

A simply laced Dynkin diagram gives rise to a family of curves over $\mathbb{Q}$ and a coregular representation, using deformations of simple singularities and Vinberg theory respectively. Thorne has conjectured and partially proven a…

The generalized Kazhdan-Lusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebra are computed explicitly. Using the result we establish a one to one correspondence between the set of…

Let G be a reductive connected p-adic group. With help of the Fourier inversion formula used in [Une formule de Plancherel pour l'algebre de Hecke d'un groupe reductif p-adique - V. Heiermann, Comm. Math. Helv. 76, 388-415, 2001] we give a…

Given a separable unital C*-algebra A, let E denote the Banach-space completion of the A-valued Schwartz space on Rn with norm induced by the A-valued inner product $<f,g>=\int f(x)^*g(x) dx$. The assignment of the pseudodifferential…

In this paper we study the complex representations of reductive groups over local non-Archimedean fields. We use the building of the reductive group to give upper-bounds for the absolute value of the character of an admissible…