Concept

Pseudo algebraically closed field

Related publications (34)

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Structure of certain Weyl modules for the Spin groups

Mikaël Cavallin

Let K be an algebraically closed field of characteristic and let W be a finite-dimensional K-vector space of dimension greater than or equal to 5. In this paper, we give the structure of certain Weyl modules for in the case where , as well as the dimension ...

2018

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

Restriction of irreducible modules for Spin2+1(K) to Spin2(K)

Mikaël Cavallin

Let K be an algebraically closed field of characteristic

p\geq0

and let

Y=SPin_{2n+1}(K) (n\geq3)

be a simply connected simple algebraic group of type

B_n

over

K

. Also let

X

be the subgroup of type

D_n

, embedded in

Y

in the usual way, as the ...

2017

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

Irreducible Geometric Subgroups of Classical Algebraic Groups

Donna Testerman, Soumaïa Nadia Ghandour

Let G be a simple classical algebraic group over an algebraically closed field K of characteristic p≥0 with natural module W. Let H be a closed subgroup of G and let V be a non-trivial irreducible tensor-indecomposable p-restricted rational KG-module such ...

American Mathematical Society2015

The torsion group of endotrivial modules

Jacques Thévenaz

Let G be a finite group and let T(G) be the abelian group of equivalence classes of endotrivial kG-modules, where k is an algebraically closed field of characteristic p. We determine, in terms of the structure of G, the kernel of the restriction map from T ...

Mathematical Science Publ2015

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

Double centralizers of unipotent elements in simple algebraic groups of type $E_7$ and $E_8$

Iulian Ion Simion

This article addresses questions about the double centralizer of unipotent elements u in simple algebraic groups G of type and defined over algebraically closed fields of bad characteristic. We use the method developed in [14] to determine , deduce its dim ...

2015

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

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

Restriction of irreducible modules for Spin2+1(K) to Spin2(K)

Mikaël Cavallin

Let K be an algebraically closed field of characteristic

p\geq0

and let

Y=SPin_{2n+1}(K) (n\geq3)

be a simply connected simple algebraic group of type

B_n

over

K

. Also let

X

be the subgroup of type

D_n

, embedded in

Y

in the usual way, as the ...

2017