Buildings of classical groups and centralizers of Lie algebra elements

Let Fo be a non-archimedean locally compact field of residual characteristic not 2. Let G be a classical group over Fo (with no quaternionic algebra involved) which is not of type An for n > 1. Let b be an element of the Lie algebra g of G that we assume semisimple for simplicity. Let H be the centralizer of b in G and h its Lie algebra. Let I and Ib denote the (enlarged) Bruhat-Tits buildings of G and H respectively. We prove that there is a natural set of maps jb : Ib ? I which enjoy the following properties: they are affine, H-equivariant, map any apartment of Ib into an apartment of I and are compatible with the Lie algebra filtrations of g and h. In a particular case, where this set is reduced to one element, we prove that jb is characterized by the last property in the list. We also prove a similar characterization result for the general linear group

Smooth representations of GL_m(D), V: Endo-classes

Let F be a locally compact nonarchimedean local field. In this article, we extend to any inner form of GL_n over F, with n>0, the notion of endo-class introduced by Bushnell and Henniart for GL_n(F). We investigate the intertwining relations of simple characters of these groups, in particular their preservation properties under transfer. This allows us to associate to any discrete series representation of an inner form of GL_n(F) an endo-class over F. We conjecture that this endo-class is invariant under the local Jacquet-Langlands correspondence

Semisimple types for p -adic classical groups

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Distinction of representations via Bruhat-Tits buildings of p-adic groups

Introductory and pedagogical treatmeant of the article : P. Broussous "Distinction of the Steinberg representation", with an appendix by Fran\c{c}ois Court\`es, IMRN 2014, no 11, 3140-3157. To appear in Proceedings of Chaire Jean Morlet, Dipendra Prasad, Volker Heiermann Ed. 2017. Contains modified and simplified proofs of loc. cit. This article is written in memory of Fran\c{c}ois Court\`es who passed away in september 2016.Comment: 33 pages, 4 figure

The supercuspidal representations of p-adic classical groups

Let G be a unitary, symplectic or special orthogonal group over a locally compact non-archimedean local field of odd residual characteristic. We construct many new supercuspidal representations of G, and Bushnell-Kutzko types for these representations. Moreover, we prove that every irreducible supercuspidal representation of G arises from our constructions.Comment: 55 pages -- minor changes from 1st version (mostly in sections 2.2, 4.2 and 6.2). To appear in Inventiones mathematicae, 2008 (DOI is not yet active as at 12 Nov 2007

Mobilise-D insights to estimate real-world walking speed in multiple conditions with a wearable device

This study aimed to validate a wearable device’s walking speed estimation pipeline, considering complexity, speed, and walking bout duration. The goal was to provide recommendations on the use of wearable devices for real-world mobility analysis. Participants with Parkinson’s Disease, Multiple Sclerosis, Proximal Femoral Fracture, Chronic Obstructive Pulmonary Disease, Congestive Heart Failure, and healthy older adults (n = 97) were monitored in the laboratory and the real-world (2.5 h), using a lower back wearable device. Two walking speed estimation pipelines were validated across 4408/1298 (2.5 h/laboratory) detected walking bouts, compared to 4620/1365 bouts detected by a multi-sensor reference system. In the laboratory, the mean absolute error (MAE) and mean relative error (MRE) for walking speed estimation ranged from 0.06 to 0.12 m/s and − 2.1 to 14.4%, with ICCs (Intraclass correlation coefficients) between good (0.79) and excellent (0.91). Real-world MAE ranged from 0.09 to 0.13, MARE from 1.3 to 22.7%, with ICCs indicating moderate (0.57) to good (0.88) agreement. Lower errors were observed for cohorts without major gait impairments, less complex tasks, and longer walking bouts. The analytical pipelines demonstrated moderate to good accuracy in estimating walking speed. Accuracy depended on confounding factors, emphasizing the need for robust technical validation before clinical application. Trial registration: ISRCTN – 12246987