Publications related to Multiplicity-free Representations of Algebraic Groups

On arithmetic progressions in symmetric sets in finite field model

We consider two problems regarding arithmetic progressions in symmetric sets in the finite field (product space) model. First, we show that a symmetric set S subset of Z(q)(n) containing vertical bar S vertical bar = mu . q(n) elements must contain at leas ...

ELECTRONIC JOURNAL OF COMBINATORICS2020

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 ...

AMER PHYSICAL SOC2020

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

of

G

, we describe the Jordan block sizes of

u

on the irreducible

G

-modules which occur as compositio ...

2019

Irreducible Subgroups of Simple Algebraic Groups – A Survey

Donna Testerman

Let G be a simple linear 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 finite dimensional irreducible rational KG-module. We say that (G,H, V) is an irreducible ...

Cambridge University Press2019

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

$A_1$-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

Generalized Norm-compatible Systems on Unitary Shimura Varieties

Mohamed Réda Boumasmoud

We define and study in terms of integral IwahoriâHecke algebras a new class of geometric operators acting on the Bruhat-Tits building of connected reductive groups over p-adic fields. These operators, which we call U-operators, generalize the geometric n ...

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

of

G

. Our ...

EPFL2018

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

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

Multiplicity-free Representations of Algebraic Groups

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On arithmetic progressions in symmetric sets in finite field model

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

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

Irreducible Subgroups of Simple Algebraic Groups – A Survey

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

$A_1$-type subgroups containing regular unipotent elements

Generalized Norm-compatible Systems on Unitary Shimura Varieties

Reductive overgroups of distinguished unipotent elements in simple algebraic groups

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

Structure of certain Weyl modules for the Spin groups

On arithmetic progressions in symmetric sets in finite field model

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

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

Irreducible Subgroups of Simple Algebraic Groups – A Survey

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

$A_1$-type subgroups containing regular unipotent elements

Generalized Norm-compatible Systems on Unitary Shimura Varieties

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

Structure of certain Weyl modules for the Spin groups

Reductive overgroups of distinguished unipotent elements in simple algebraic groups