8 citations · 10 across the 11 of their papers we have counts for
14 papers
-complete reducibility and saturation
Michael Bate, Sören Böhm, Alastair Litterick +2
Let be connected reductive linear algebraic groups defined over an algebraically closed field of characteristic . In our first main theorem we show that if a…
Condorcet Domains of Degree at most Seven
Dolica Akello-Egwell, Charles Leedham-Green, Alastair Litterick +2
In this paper we give the first explicit enumeration of all maximal Condorcet domains on alternatives. This has been accomplished by developing a new algorithm for constr…
Complete reducibility in bad characteristic
Alastair J. Litterick, Adam R. Thomas
Let be a simple algebraic group of exceptional type over an algebraically closed field of characteristic . This paper continues a long-standing effort to classify the co…
Elementary abelian subgroups: from algebraic groups to finite groups
Jianbei An, Heiko Dietrich, Alastair J. Litterick
We describe a new approach for classifying conjugacy classes of elementary abelian subgroups in simple algebraic groups over an algebraically closed field, and understanding the no…
Complete reducibility and subgroups of exceptional algebraic groups
Alastair J. Litterick, David I. Stewart, Adam R. Thomas
This survey article has two components. The first part gives a gentle introduction to Serre's notion of -complete reducibility, where is a connected reductive algebraic grou…
Complete reducibility of subgroups of reductive algebraic groups over nonperfect fields IV: An example
Falk Bannuscher, Alastair Litterick, Tomohiro Uchiyama
Let be a nonperfect separably closed field. Let be a connected reductive algebraic group defined over . We study rationality problems for Serre's notion of complete redu…
Complete reducibility: Variations on a theme of Serre
Maike Gruchot, Alastair Litterick, Gerhard Roehrle
In this note, we unify and extend various concepts in the area of -complete reducibility, where is a reductive algebraic group. By results of Serre and Bate--Martin--Röhrle,…
Rigid representations of triangle groups
Alastair Litterick, Benjamin Martin
We prove a generalization of a conjecture of C. Marion on generation properties of finite groups of Lie type, by considering geometric properties of an appropriate representation v…
Relative complete reducibility and normalised subgroups
Maike Gruchot, Alastair Litterick, Gerhard Roehrle
We study a relative variant of Serre's notion of -complete reducibility for a reductive algebraic group . We let be a reductive subgroup of , and consider subgroups of…
Further Rigid Triples of Classes in
Matthew Conder, Alastair Litterick
We establish the existence of two rigid triples of conjugacy classes in the algebraic group in characteristic , complementing results of the second author with Liebeck a…
Reducible subgroups of exceptional algebraic groups
Alastair J. Litterick, Adam R. Thomas
Let be a simple algebraic group over an algebraically closed field. A closed subgroup of is called -completely reducible (-cr) if, whenever is contained in a…
On finite simple images of triangle groups
Sebastian Jambor, Alastair Litterick, Claude Marion
For a simple algebraic group G in characteristic p, a triple (a,b,c) of positive integers is said to be rigid for G if the dimensions of the subvarieties of G of elements of order…
On Non-Generic Finite Subgroups of Exceptional Algebraic Groups
Alastair J. Litterick
The study of finite subgroups of a simple algebraic group reduces in a sense to those which are almost simple. If an almost simple subgroup of has a socle which is not isom…
Complete Reducibility in Good Characteristic
Alastair J. Litterick, Adam R. Thomas
Let be a simple algebraic group of exceptional type, over an algebraically closed field of characteristic . A closed subgroup of is called -completely reduc…