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Person# Martin W. Liebeck

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Algebraic group

In mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs bot

Reductive group

In mathematics, a reductive group is a type of linear algebraic group over a field. One definition is that a connected linear algebraic group G over a perfect field is reductive if it has a represen

Linear algebraic group

In mathematics, a linear algebraic group is a subgroup of the group of invertible n\times n matrices (under matrix multiplication) that is defined by polynomial equations. An example i

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Martin W. Liebeck, Claude Marion

We produce a rigid triple of classes in the algebraic group G(2) in characteristic 5, and use it to show that the finite groups G(2)(5(n)) are not (2, 5, 5)-generated.

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We continue our work, started in [9], on the program of classifying triples (X, Y, V), where X, Yare simple algebraic groups over an algebraically closed field of characteristic zero with X < Y, and Vis an irreducible module for Y such that the restriction V down arrow X is multiplicity-free. In this paper we handle the case where X is of type A, and is irreducibly embedded in Y of type B, C or D. It turns out that there are relatively few triples for X of arbitrary rank, but a number of interesting exceptional examples arise for small ranks. (c) 2021 Elsevier Inc. All rights reserved.

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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 element of G to a distinguished element of I(V). We also settle a base case of the general problem of determining when the restriction of ρ to a simple subgroup of G is multiplicity-free.

2015