Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

Algebres de lie semi‐simples complexes

© Association des collaborateurs de Nicolas Bourbaki, 1961, tous droits réservés. L’accès aux archives du séminaire Bourbaki (http://www.bourbaki. ens.fr/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Sur les intégrales attachées aux formes automorphes

Analyse harmonique dans les systèmes de Tits bornologiques de type affine

/pdf/invariant-theory-for-generalized-root-systems-looijenganolun-1f1gjtoonq.pdf

Invariant Theory for Generalized Root Systems : Looijengaの論文(Preprint)の紹介 (リー環,代数群とその周辺)

In this paper, we prove some finiteness results about split Kac-Moody groups over local non-archimedean fields. Our results generalize those of "An affine Gindikin-Karpelevich formula" by Alexander Braverman, Howard Garland, David Kazhdan and Manish Patnaik. We do not require our groups to be affine. We use the hovel I associated to this situation, which is the analogue of the Bruhat-Tits building for a reductive group.

https://hal.archives-ouvertes.fr/hal-01248091/document

Gindikin-Karpelevich finiteness for Kac-Moody groups over local fields

A masure (a.k.a affine ordered hovel) I is a generalization of the Bruhat-Tits building that is associated to a split Kac-Moody group G over a non-archimedean local field. This is a union of affine spaces called apartments. When G is a reductive group, I is a building and there is a G-invariant distance inducing a norm on each apartment. In this paper, we study distances on I inducing the affine topology on each apartment. We show that some properties (completeness, local compactness, ...) cannot be satisfyed when G is not reductive. Nevertheless, we construct distances such that each element of G is a continuous automorphism of I.

pdf/distances-on-a-masure-affine-ordered-hovel-z6rvxzzz3k.pdf

Distances on a masure (affine ordered hovel)

Masures are generalizations of Bruhat-Tits buildings. They were introduced to study Kac-Moody groups over ultrametric fields, which generalize reductive groups over the same fields. If A and A are two apartments in a building, their intersection is convex (as a subset of the finite dimensional affine space A) and there exists an isomorphism from A to A fixing this intersection. We study this question for masures and prove that the analogous statement is true in some particular cases. We deduce a new axiomatic of masures, simpler than the one given by Rousseau.

Convexity in a masure

Let G be a split Kac-Moody group over a non-archimedean local field. We define a completion of the Iwahori-Hecke algebra of G. We determine its center and prove that it is isomorphic to the spherical Hecke algebra of G using the Satake isomorphism. This is thus similar to the situation of reductive groups. Our main tool is the masure I associated to this setting, which is the analogue of the Bruhat-Tits building for reductive groups. Then, for each special and spherical facet F, we associate a Hecke algebra. In the Kac-Moody setting, this construction was known only for the spherical subgroup and for the Iwahori subgroup.

pdf/completed-iwahori-hecke-algebras-and-parahorical-hecke-555j7hwvxu.pdf

Completed Iwahori-Hecke algebras and parahorical Hecke algebras for Kac-Moody groups over local fields

Masures were introduced in 2008 by Gaussent and Rousseau in order to study Kac-Moody groups over local fields. They generalize Bruhat-Tits buildings. In this thesis, we study the properties of masures and the application of the theory of masures in arithmetic and representation theory.
Rousseau gave an axiomatic of masures, inspired by the definition by Tits of Bruhat-Tits buildings. We propose an axiomatic, which is simpler and easier to handle and we prove that this axiomatic is equivalent to the one of Rousseau.
We study (in collaboration with Ramla Abdellatif) the spherical and Iwahori-Hecke algebras introduced by Bardy-Panse, Gaussent and Rousseau. We prove that on the contrary to the reductive case, the center of the Iwahori-Hecke algebra is almost trivial and is in particular not isomorphic to the spherical Hecke algebra. We thus introduce a completed Iwahori-Hecke algebra, whose center is isomorphic to the spherical Hecke algebra. We also associate Hecke algebras to spherical faces between 0 and the fundamental alcove of the masure, generalizing the construction of Bardy-Panse, Gaussent and Rousseau of the Iwahori-Hecke algebra.
The Gindikin-Karpelevich formula is an important formula in the theory of reductive groups over local fields. Recently, Braverman, Garland, Kazhdan and Patnaik generalized this formula to the case of affine Kac-Moody groups. An important par of their prove consists in proving that this formula is well-defined, which means that the numbers involved in this formula, which are the cardinals of certain subgroup of quotients of the studied subgroup are finite. We prove this finiteness in the case of general Kac-Moody groups.
We also study distances on a masure. I prove that there is no distance having the same properties as in the reductive case. We construct distances having weaker properties, but which seem interesting.

https://hal.archives-ouvertes.fr/tel-01856620/document

Study of masures and of their applications in arithmetic

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