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Concept

Lie group

Related publications (29)

Multiplicity-free Representations of Algebraic Groups

Donna Testerman

Let K be an algebraically closed field of characteristic zero, and let G be a connected reductive algebraic group over K. We address the problem of classifying triples (G, H, V ), where H is a proper connected subgroup of G, and V is a finitedimensional ir ...

Amer Mathematical Soc2024

Touch and Closeness in Naturally Organized Activities

Alain Bovet

Countless aspects of touch and closeness have been questioned in an unprecedented way during the recent Covid epidemic. Social practices as banal as greetings were both reflexively and practically challenged and sometimes deeply altered, resulting in painf ...

2024

Lie groups in the symmetric group: Reducing Ulam's problem to the simple case

Nicolas Monod

Ulam asked whether all Lie groups can be represented faithfully on a countable set. We establish a reduction of Ulam's problem to the case of simple Lie groups. In particular, we solve the problem for all solvable Lie groups and more generally Lie groups w ...

Academic Press Inc Elsevier Science2023

Unlikely intersections on the p-adic formal ball

Vlad Serban

We investigate generalizations along the lines of the Mordell-Lang conjecture of the author's p-adic formal Manin-Mumford results for n-dimensional p-divisible formal groups F. In particular, given a finitely generated subgroup (sic) of F(Q(p)) and a close ...

SPRINGER INT PUBL AG2023

Duality and bicrystals on infinite binary matrices

Thomas Gerber

The set of finite binary matrices of a given size is known to carry a finite type AA bicrystal structure. We first review this classical construction, explain how it yields a short proof of the equality between Kostka polynomials and one-dimensional sums t ...

EMS Press2023

Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups

Nicolas Monod

We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of orientation-preserving homeomorphisms of the circle and of the closed 2-disc, it is isomorphic to the polynomial ring g ...

SPRINGER HEIDELBERG2023

Lie groups as permutation groups: Ulam's problem in the nilpotent case

Nicolas Monod

Ulam asked whether every connected Lie group can be represented on a countable structure. This is known in the linear case. We establish it for the first family of non-linear groups, namely in the nilpotent case. Further context is discussed to illustrate ...

WALTER DE GRUYTER GMBH2022

A b-symplectic slice theorem

Anna Kiesenhofer

In this article, motivated by the study of symplectic structures on manifolds with boundary and the systematic study of b-symplectic manifolds started in Guillemin, Miranda, and Pires Adv. Math. 264 (2014), 864-896, we prove a slice theorem for Lie group a ...

WILEY2022

Effect of Different Communication Affordances on the Emergence of Collaboration Strategies in an Online Multiplayer Game

Pierre Dillenbourg, Barbara Bruno, Aditi Kothiyal, Hala Khodr

In a group, the collective dynamics is governed by the inter- actions between individuals, which can manifest differently depending on the available means of communication. In this paper, we compare 3 conditions of communication affordances (global chat, l ...

Springer2022

The Cen A galaxy group: Dynamical mass and missing baryons

Oliver Müller

The nearby elliptical galaxy Centaurus A (Cen A) is surrounded by a flattened system of dwarf satellite galaxies with coherent motions. Using a novel Bayesian approach, we measured the mean rotation velocity nu(rot) and velocity dispersion sigma(int) of th ...

EDP SCIENCES S A2022

Fourier non-uniqueness sets from totally real number fields

Martin Peter Stoller

Let K be a totally real number field of degree n >= 2. The inverse different of K gives rise to a lattice in Rn. We prove that the space of Schwartz Fourier eigenfunctions on R-n which vanish on the "component-wise square root" of this lattice, is infinite ...

EUROPEAN MATHEMATICAL SOC-EMS2022

A Hopf algebra model for Dwyer's tame spaces

Haoqing Wu

In this thesis, we give a modern treatment of Dwyer's tame homotopy theory using the language of

\infty

-categories. We introduce the notion of tame spectra and show it has a concrete algebraic description. We then carry out a study of

\infty

-operads an ...

EPFL2022

Spherical birational sheets in reductive groups

Filippo Ambrosio

We classify the spherical birational sheets in a complex simple simply-connected algebraic group. We use the classification to show that, when G is a connected reductive complex algebraic group with simply-connected derived subgroup, two conjugacy classes ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2021

Almost impossible E_8 and Leech lattices

Maryna Viazovska

We start this short note by introducing two remarkable mathematical objects: the E8E8 root lattice Lambda8Lambda8 in 8-dimensional Euclidean space and the Leech lattice Lambda24Lambda24 in 24-dimensional space. These two lattices stand out among their lat ...

2021

Subgroups of elliptic elements of the Cremona group

Christian Lucius Urech

The Cremona group is the group of birational transformations of the complex projective plane. In this paper we classify its subgroups that consist only of elliptic elements using elementary model theory. This yields in particular a description of the struc ...

2021

On complete reducibility of tensor products of simple modules over simple algebraic groups

Jonathan Gruber

Let G be a simply connected simple algebraic group over an al- gebraically closed ﬁeld k of characteristic p > 0. The category of rationalG-modules is not semisimple. We consider the question of when the tensorproduct of two simple G-modules L(λ) and L(μ) ...

2021

Home, Spatial Familiarity And Routines In Mobility Behaviours

Marc-Edouard Baptiste Grégoire Schultheiss

This research explores the unreasoned influences of locational behaviour – i.e. locational habits – in Activity- Travel-Behaviour (ATB). In particular, the interrelations between Activity Space characteristics and mobility patterns. In a wider research eff ...

2021

Robust Differentiable SVD

Pascal Fua, Mathieu Salzmann, Wei Wang, Yinlin Hu, Zheng Dang

Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power Iteration (PI) ...

2021

Development of remote C-H bond functionalization of redox-active alcohol derivatives and oxidative transformations under photoredox catalysis

Alexandre Julien Florent Leclair

The development of radical-based remote C(sp3)-H functionalizations of redox-active alcohol derivatives, oxidative cycloaddition and rearrangement transformations under visible light photocatalysis constitute the basis of this thesis. The first chapter des ...

EPFL2021