Matching of orbital integrals (transfer) and Roche Hecke algebra isomorphisms

Let $F$ be a non-Archimedan local field, $G$ a connected reductive group defined and split over $F$, and $T$ a maximal $F$-split torus in $G$. Let $\chi_0$ be a depth zero character of the maximal compact subgroup $\mathcal{T}$ of $T(F)$. It gives by inflation a character $\rho$ of an Iwahori subgroup $\mathcal{I}$ of $G(F)$ containing $\mathcal{T}$. From Roche, $\chi_0$ defines a split endoscopic group $G'$ of $G$, and there is an injective morphism of ${\Bbb C}$-algebras $\mathcal{H}(G(F),\rho) \rightarrow \mathcal{H}(G'(F),1_{\mathcal{I}'})$ where $\mathcal{H}(G(F),\rho)$ is the Hecke algebra of compactly supported $\rho^{-1}$-spherical functions on $G(F)$ and $\mathcal{I}'$ is an Iwahori subgroup of $G'(F)$. This morphism restricts to an injective morphism $\zeta: \mathcal{Z}(G(F),\rho)\rightarrow \mathcal{Z}(G'(F),1_{\mathcal{I}'})$ between the centers of the Hecke algebras. We prove here that a certain linear combination of morphisms analogous to $\zeta$ realizes the transfer (matching of strongly $G$-regular semisimple orbital integrals). If ${\rm char}(F)=p>0$, our result is unconditional only if $p$ is large enough.Comment: 82 page

Homothetic interval orders

N*-set, semigroup, weak order, semiorder, interval order, intransitive indifference, independence, homothetic structure, representation

Biased representation of homothetic preferences on homogeneous sets

In the homogeneous case of one-dimensional objects, we show that any preference relation that is positive and homothetic can be represented by a quantitative utility function and unique bias. This bias may favor or disfavor the preference for an object. In the first case, preferences are complete but not transitive and an object may be preferred even when its utility is lower. In the second case, preferences are asymmetric and transitive but not negatively transitive and it may not be sufficient for an object to have a greater utility for be preferred. In this manner, the bias reflects the extent to which preferences depart from the maximization of a utility function.Intransitive preferences, incomplete preferences, irrational behavior, bias, procedural concerns, process of choice

Biased quantitative measurement of interval ordered homothetic preferences

We represent interval ordered homothetic preferences with a quantitative homothetic utility function and a multiplicative bias. When preferences are weakly ordered (i.e. when indifference is transitive), such a bias equals 1. When indifference is intransitive, the biasing factor is a positive function smaller than 1 and measures a threshold of indifference. We show that the bias is constant if and only if preferences are semiordered, and we identify conditions ensuring a linear utility function. We illustrate our approach with indifference sets on a two dimensional commodity space.Weak order, semiorder, interval order, intransitive indifference, independence, homothetic, representation, linear utility

Causes and effects of World War I.

Thesis (Ed.M.)--Boston Universit

La transformée de Fourier pour les espaces tordus sur un groupe réductif p-adique

le papier a été accepté dans la revue Astérisque— Let G be a connected reductive group defined over a non–Archimedean local field F. Put G = G(F). Let θ be an F –automorphism of G, and let ω be a smooth character of G. This paper is concerned with the smooth complex representations π of G such that π θ = π • θ is isomorphic to ωπ = ω ⊗ π. If π is admissible, in particular irreducible, the choice of an isomorphism A from ωπ to π θ (and of a Haar measure on G) defines a distribution Θ A π = tr(π • A) on G. The twisted Fourier transform associates to a compactly supported locally constant function f on G, the function (π, A) → Θ A π (f) on a suitable Grothendieck group. Here we describe its image (Paley– Wiener theorem) and its kernel (spectral density theorem).Soit G un groupe réductif connexe défini sur un corps local non ar-chimédien F. On pose G = G(F). Soit aussi θ un F –automorphisme de G, et ω un caractère lisse de G. On s'intéresse aux représentations complexes lisses π de G telles que π θ = π • θ est isomorphe à ωπ = ω ⊗ π. Si π est admissible, en particulier irréductible, le choix d'un isomorphisme A de ωπ sur π θ (et d'une mesure de Haar sur G) définit une distribution Θ A π = tr(π • A) sur G. La transformée de Fourier tordue associe à une fonction f sur G localement constante et à support compact, la fonction (π, A) → Θ A π (f) sur un groupe de Grothendieck adéquat. On décrit ici son image (théorème de Paley–Wiener) et son noyau (théorème de densité spectrale)

Le lemme fondamental pour l'endoscopie tordue: le cas où le groupe endoscopique non ramifié est un tore

We prove the fundamental lemma for twisted endoscopy, for the unit elements of the spherical Hecke algebras, in the case of a non ramified elliptic endo- scopic datum whose underlying group is a torus. This implies that the fundamental lemma for twisted endoscopy is now proved, for all elements in the spherical Hecke algebras, in characteristic zero and any residue characteristic

Homothetic interval orders

AbstractWe give a characterization of the non-empty binary relations ≻ on a N*-set A such that there exist two morphisms of N*-sets u1,u2:A→R+ verifying u1⩽u2 and x≻y⇔u1(x)>u2(y). They are called homothetic interval orders. If ≻ is a homothetic interval order, we also give a representation of ≻ in terms of one morphism of N*-sets u:A→R+ and a map σ:u-1(R+*)×A→R+* such that x≻y⇔σ(x,y)u(x)>u(y). The pairs (u1,u2) and (u,σ) are “uniquely” determined by ≻, which allows us to recover one from each other. We prove that ≻ is a semiorder (resp. a weak order) if and only if σ is a constant map (resp. σ=1). If moreover A is endowed with a structure of commutative semigroup, we give a characterization of the homothetic interval orders ≻ represented by a pair (u,σ) so that u is a morphism of semigroups