Publications associées à Objet exceptionnel

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

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

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

Maximal subgroups acting with two composition factors on irreducible representations of exceptional algebraic groups

Nathan Scheinmann

Let

Y

be a simply connected simple algebraic group over an algebraically closed field

k

of characteristic

p

and let

X

be a maximal closed connected simple subgroup of

Y

. Excluding some small primes in specific cases, we classify the

p

-restrict ...

EPFL2019

Perfect soliton crystals in optical microresonators

Tobias Kippenberg, Junqiu Liu, Maxim Karpov, Hairun Guo, Martin Hubert Peter Pfeiffer, Wenle Weng

We demonstrate the existence of perfect soliton crystal states and develop the deterministic procedure for their excitation in Si3N4 microresonators. We show that despite exceptional symmetrical properties, their behavior is strongly linked to the chaotic ...

IEEE2019

Irreducible representations of simple algebraic groups in which a unipotent element is represented by a matrix with a single non-trivial Jordan block

Donna Testerman

Let G be a simply connected simple linear algebraic group of exceptional Lie type over an algebraically closed field F of characteristic p >= 0, and let u is an element of G be a non-identity unipotent element. Let phi be a non-trivial irreducible represen ...

2018

Reductive overgroups of distinguished unipotent elements in simple algebraic groups

Mikko Tapani Korhonen

Let

G

be a simple linear algebraic group over an algebraically closed field

K

of characteristic

p \geq 0

. In this thesis, we investigate closed connected reductive subgroups

X < G

that contain a given distinguished unipotent element

u

of

G

. Our ...

EPFL2018

Closing Large Hyperbolic 2g-gons : a Way to Study Hyperelliptic Riemann Surfaces of Genus g

Poincaré's uniformisation theorem says that any Riemann surface is conformally equivalent to a unique (up to isometry) surface of constant Gauss curvature 0, 1 or –1. The (topologically) richest of these three worlds is for curvature –1 formed of hyperboli ...

EPFL2012

Triangle generation of finite exceptional groups of low rank

Claude Marion

Given a triple (p(1), p(2), p(3)) of primes, the object of this paper is the study of the space Hom(T-p1,T-p2,T-p3, G) of homomorphisms from the triangle group T-p1,T-p2,T-p3 to a finite simple exceptional group G of Lie type B-2(2), (2)G(2), G(2) or D-3(4 ...

Elsevier2011

Degree and valuation of the Schur elements of cyclotomic Hecke algebras

Following the generalization of the notion of families of characters, defined by Lusztig for Weyl groups, to the case of complex reflection groups, thanks to the definition given by Rouquier, we show that the degree and the valuation of the Schur elements ...

Elsevier2008