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Concept

Unipotent

Related publications (15)

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

Exploiting Marginal Stability in Slow-Fast Quasilinear Dynamical Systems

Alessia Ferraro

The accurate investigation of many geophysical phenomena via direct numerical simulations is computationally not possible nowadays due to the huge range of spatial and temporal scales to be resolved. Therefore advances in this field rely on the development ...

EPFL2022

Orders That Are Etale-Locally Isomorphic

Eva Bayer Fluckiger, Mathieu Huruguen

Let R be a semilocal Dedekind domain with fraction field F. It is shown that two hereditary R-orders in central simple F-algebras that become isomorphic after tensoring with F and with some faithfully flat etale R-algebra are isomorphic. On the other hand, ...

AMER MATHEMATICAL SOC2020

Minimal Polynomials Of Unipotent Elements Of Non-Prime Order In Irreducible Representations Of The Exceptional Algebraic Groups In Some Good Characteristics

Donna Testerman

In a number of cases the minimal polynomials of the images of unipotent elements of non-prime order in irreducible representations of the exceptional algebraic groups in good characteristics are found. It is proved that if p > 5 for a group of type E-8 and ...

2019

Jordan blocks of unipotent elements in some irreducible representations of classical groups in good characteristic

Mikko Tapani Korhonen

Let

G

be a classical group with natural module

V

over an algebraically closed field of good characteristic. For every unipotent element

u

G

, we describe the Jordan block sizes of

u

on the irreducible

G

-modules which occur as compositio ...

American Mathematical Society (AMS)2019

Orders that are étale-locally isomorphic

Eva Bayer Fluckiger, Mathieu Huruguen

Let R be a semilocal Dedekind domain with fraction field F. It is shown that two hereditary R-orders in central simple F-algebras that become isomorphic after tensoring with F and with some faithfully flat étale R-algebra are isomorphic. On the other hand, ...

2019

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

G

. Our ...

EPFL2018

On the fundamental domain of affine Springer fibers

Zongbin Chen

Let G be a connected reductive algebraic group over an algebraically closed field k,gamma is an element of g( k(( epsilon ))) a semisimple regular element, we introduce a fundamental domain F gamma for the affine Springer fibers X gamma. We show that the p ...

Springer Heidelberg2017

Double centralizers of unipotent elements in simple algebraic groups of type G2, F4 and E6

Iulian Ion Simion

Let

u

be a unipotent element of a simple algebraic group

G

over a field

k

of characteristic

p

. We develop a method for computing the connected component of

Z(C_G(u))

in the cases where

p

is positive and both it and the rank of

G

are small eno ...

2013

Irreducibility In Algebraic Groups And Regular Unipotent Elements

Donna Testerman

We study (connected) reductive subgroups G of a reductive algebraic group H, where G contains a regular unipotent element of H. The main result states that G cannot lie in a proper parabolic subgroup of H. This result is new even in the classical case H = ...

American Mathematical Society (AMS)2013

Le foncteur de bi-ensembles des modules de p-permutation

Mélanie Baumann

Let k be an algebraically closed field of characteristic p, where p is a prime number or 0. Let G be a finite group and ppk(G) be the Grothendieck group of p-permutation kG-modules. If we tensor it with C, then Cppk becomes a C-linear biset functor. Recall ...

EPFL2012

Centres of centralizers of unipotent elements in simple algebraic groups

Donna Testerman

Let G be a simple algebraic group defined over an algebraically closed field k whose characteristic is either 0 or a good prime for G, and let u is an element of G be unipotent. We study the centralizer C-G(u), especially its centre Z(C-G(u)). We calculate ...

2011

Nilpotent centralizers and Springer isomorphisms

Donna Testerman

Let GG be a semisimple algebraic group over a field KK whose characteristic is very good for GG, and let σσ be any GG-equivariant isomorphism from the nilpotent variety to the unipotent variety; the map σσ is known as a Springer isomorphism. Let y∈G(K)y∈G( ...

2009

On Haagerup and Kazhdan properties

Yves de Cornulier

In the first chapter, we characterize p-adic linear algebraic groups with the Haagerup Property. We also characterize connected Lie groups having the Haagerup Property viewed as discrete groups, and we provide an example of a finitely presented group not h ...

EPFL2006

Related publications (15)

Multiplicity-free Representations of Algebraic Groups

Donna Testerman

Amer Mathematical Soc2024

Exploiting Marginal Stability in Slow-Fast Quasilinear Dynamical Systems

Alessia Ferraro

EPFL2022

Orders That Are Etale-Locally Isomorphic

Eva Bayer Fluckiger, Mathieu Huruguen

AMER MATHEMATICAL SOC2020

Minimal Polynomials Of Unipotent Elements Of Non-Prime Order In Irreducible Representations Of The Exceptional Algebraic Groups In Some Good Characteristics

Donna Testerman

2019

Jordan blocks of unipotent elements in some irreducible representations of classical groups in good characteristic

Mikko Tapani Korhonen

Let

G

be a classical group with natural module

V

over an algebraically closed field of good characteristic. For every unipotent element

u

G

, we describe the Jordan block sizes of

u

on the irreducible

G

-modules which occur as compositio ...

American Mathematical Society (AMS)2019

Orders that are étale-locally isomorphic

Eva Bayer Fluckiger, Mathieu Huruguen

Let R be a semilocal Dedekind domain with fraction field F. It is shown that two hereditary R-orders in central simple F-algebras that become isomorphic after tensoring with F and with some faithfully flat étale R-algebra are isomorphic. On the other hand, ...

2019