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Concept

Borel subgroup

Related publications (17)

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

Nonlinear optical diode effect in a magnetic Weyl semimetal

Philip Johannes Walter Moll, Chunyu Guo

Diode effects are of great interest for both fundamental physics and modern technologies. Electrical diode effects (nonreciprocal transport) have been observed in Weyl systems. Optical diode effects arising from the Weyl fermions have been theoretically co ...

Nature Portfolio2024

$A_1$-type subgroups containing regular unipotent elements

Donna Testerman

Let be a simple exceptional algebraic group of adjoint type over an algebraically closed field of characteristic and let be a subgroup of containing a regular unipotent element of . By a theorem of Testerman, is contained in a connected subgroup of of type ...

2019

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

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 irreducible subgroups of simple algebraic groups

Donna Testerman, Claude Marion

Let G be a simple algebraic group over an algebraically closed field K of characteristic p >= 0, let H be a proper closed subgroup of G and let V be a nontrivial irreducible KG-module, which is p-restricted, tensor indecomposable and rational. Assume that ...

Springer Heidelberg2017

Toda frames, harmonic maps and extended Dynkin diagrams

Katharine Felicity Turner

We consider a natural subclass of harmonic maps from a surface into G/T, namely cyclic primitive maps. Here G is any simple real Lie group (not necessarily compact), T is a Cartan subgroup and both are chosen so that there is a Coxeter automorphism on G(C) ...

Elsevier2017

Central Subalgebras Of The Centralizer Of A Nilpotent Element

Donna Testerman

Let G be a connected, semisimple algebraic group over a field k whose characteristic is very good for G. In a canonical manner, one associates to a nilpotent element X is an element of Lie(G) a parabolic subgroup P - in characteristic zero, P may be descri ...

American Mathematical Society (AMS)2016

Restricting representations of classical algebraic groups to maximal subgroups

Mikaël Cavallin

Fix an algebraically closed field

K

having characteristic

p\geq 0

and let

Y

be a simple algebraic group of classical type over

K.

Also let

X

be maximal among closed connected subgroups of

Y

and consider a non-trivial

p

-restricted irreducible ...

EPFL2015

Subgroups Of Simple Algebraic Groups Containing Regular Tori, And Irreducible Representations With Multiplicity 1 Non-Zero Weights

Donna Testerman

Our main goal is to determine, under certain restrictions, the maximal closed connected subgroups of simple linear algebraic groups containing a regular torus. We call a torus regular if its centralizer is abelian. We also obtain some results of independen ...

Springer Verlag2015

Distinguished unipotent elements and multiplicity-free subgroups of simple algebraic groups

Donna Testerman

For G a simple algebraic group over an algebraically closed field of characteristic 0, we determine the irreducible representations ρ:G→I(V), where I(V) denotes one of the classical groups SL(V), Sp(V), SO(V), such that ρ sends some distinguished unipotent ...

2015

The xi-stability on the affine grassmannian

Zongbin Chen

We introduce a notion of xi-stability on the affine grassmannian (SIC) for the classical groups, this is the local version of the xi-stability on the moduli space of Higgs bundles on a curve introduced by Chaudouard and Laumon. We prove that the quotient ( ...

Springer Heidelberg2015

Embeddings Of Maximal Tori In Orthogonal Groups

Eva Bayer Fluckiger

We give necessary and sufficient conditions for an orthogonal group defined over a global field of characteristic not equal 2 to contain a maximal torus of a given type. ...

Annales Inst Fourier2014

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

Nilpotent subalgebras of semisimple Lie algebras

Donna Testerman

Let g be the Lie algebra of a semisimple linear algebraic group. Under mild conditions on the characteristic of the underlying field, one can show that any subalgebra of g consisting of nilpotent elements is contained in some Borel subalgebra. In this Note ...

2009

Irreducibility of disconnected subgroups of exceptional algebraic groups

Soumaïa Nadia Ghandour

This dissertation is concerned with the study of irreducible embeddings of simple algebraic groups of exceptional type. It is motivated by the role of such embeddings in the study of positive dimensional closed subgroups of classical algebraic groups. The ...

EPFL2008

Extrapolation et synthèse

Christian Fiorillo

Let G a locally compact group, H a closed subgroup and 1 < p < ∞. It's well-known that the restriction of the functions from G to H is a surjective linear contraction from Ap(G) onto Ap(H). We prove, when H is amenable, that every element in Ap(H) with com ...

EPFL2007

Related publications (17)

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

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

K

having characteristic

p\geq 0

and let

Y

be a simple algebraic group of classical type over

K.

Also let

X

be maximal among closed connected subgroups of

Y

and consider a non-trivial

p

-restricted irreducible ...

EPFL2015

Subgroups Of Simple Algebraic Groups Containing Regular Tori, And Irreducible Representations With Multiplicity 1 Non-Zero Weights

Donna Testerman

Springer Verlag2015

Annales Inst Fourier2014