Publications associées à Generalized Blocks of Unipotent Characters in the Finite General Linear Group

Multiplicity-free Representations of Algebraic Groups

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

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

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

Eigenvalue multiplicities of group elements in irreducible representations of simple linear algebraic groups

Ana-Maria Retegan

Let k be an algebraically closed field of arbitrary characteristic, let G be a simple simply connected linear algebraic group and let V be a rational irreducible tensor-indecomposable finite-dimensional kG-module. For an element g of G we denote by $V_{g}( ...

EPFL2022

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

Generic direct summands of tensor products for simple algebraic groups and quantum groups at roots of unity

Jonathan Gruber

Let G be either a simple linear algebraic group over an algebraically closed field of characteristic l>0 or a quantum group at an l-th root of unity. The category Rep(G) of finite-dimensional G-modules is non-semisimple. In this thesis, we develop new tech ...

EPFL2022

From Trees to Barcodes and Back Again: A Combinatorial, Probabilistic and Geometric Study of a Topological Inverse Problem

Adélie Eliane Garin

In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial, geometric, probabilistic and statistical point of view. Computing the persistent homology of a merge tree yields a barcode B. Reconstructing a tree from B invol ...

EPFL2022

Coxeter Combinatorics For Sum Formulas In The Representation Theory Of Algebraic Groups

Jonathan Gruber

Let G be a simple algebraic group over an algebraically closed field F of characteristic p >= h, the Coxeter number of G. We observe an easy 'recursion formula' for computing the Jantzen sum formula of a Weyl module with p-regular highest weight. We also d ...

AMER MATHEMATICAL SOC2022

Spectra of non-regular elements in irreducible representations of simple algebraic groups

Donna Testerman

We study the spectra of non-regular semisimple elements in irreducible representations of simple algebraic groups. More precisely, we prove that if G is a simply connected simple linear algebraic group and φ : G → GL(V ) is a non-trivial irreducible repres ...

2021

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

Optimal radial basis for density-based atomic representations

Félix Benedito Clément Musil, Michele Ceriotti, Alexander Jan Goscinski, Jigyasa Nigam, Sergey Pozdnyakov

The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular representations ...

2021

Local invertibility and sensitivity of atomic structure-feature mappings

Michele Ceriotti, Sergey Pozdnyakov

Background: The increasingly common applications of machine-learning schemes to atomic-scale simulations have triggered efforts to better understand the mathematical properties of the mapping between the Cartesian coordinates of the atoms and the variety o ...

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

Arithmetically rigid schemes via deformation theory of equivariant vector bundles

Maciej Emilian Zdanowicz

We analyze the deformation theory of equivariant vector bundles. In particular, we provide an effective criterion for verifying whether all infinitesimal deformations preserve the equivariant structure. As an application, using rigidity of the Frobenius ho ...

SPRINGER HEIDELBERG2021

On arithmetic progressions in symmetric sets in finite field model

Jan Hazla

We consider two problems regarding arithmetic progressions in symmetric sets in the finite field (product space) model. ...

ELECTRONIC JOURNAL OF COMBINATORICS2020

Approximating nonabelian free groups by groups of homeomorphisms of the real line

Yash Lodha

We show that for a large class C of finitely generated groups of orientation preserving homeomorphisms of the real line, the following holds: Given a group G of rank k in C, there is a sequence of k-markings (G,S-n), n is an element of N whose limit in the ...

2020

Coherent actions by homeomorphisms on the real line or an interval

Yash Lodha

We study actions of groups by orientation preserving homeomorphisms on R (or an interval) that are minimal, have solvable germs at +/-infinity and contain a pair of elements of a certain dynamical type. We call such actions coherent. We establish that such ...

HEBREW UNIV MAGNES PRESS2020

Simple groups of birational transformations in dimension two

Christian Lucius Urech

We classify simple groups that act by birational transformations on compact complex Kahler surfaces. Moreover, we show that every finitely generated simple group that acts non-trivially by birational transformations on a projective surface over an arbitrar ...

2020

Haldane Gap of the Three-Box Symmetric SU(3) Chain

Frédéric Mila, Samuel Gozel, Pierre Marcel Nataf

Motivated by the recent generalization of the Haldane conjecture to SU(3) chains [Lajko et al., Nucl. Phys. B924, 508 (2017)] according to which a Haldane gap should be present for symmetric representations if the number of boxes in the Young diagram is a ...

2020

From Trees to Barcodes and Back Again: Theoretical and Statistical Perspectives

Kathryn Hess Bellwald, Lida Kanari, Adélie Eliane Garin

Methods of topological data analysis have been successfully applied in a wide range of fields to provide useful summaries of the structure of complex data sets in terms of topological descriptors, such as persistence diagrams. While there are many powerful ...

2020