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Double centralizers of unipotent elements in simple algebraic groups of type G2, F4 and E6
Related publications (38)
$A_1$-type subgroups containing regular unipotent elements
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 ...
2019Irreducible Subgroups of Simple Algebraic Groups – A Survey
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 Press2019Minimal Polynomials Of Unipotent Elements Of Non-Prime Order In Irreducible Representations Of The Exceptional Algebraic Groups In Some Good Characteristics
In a number of cases the minimal polynomials of the images of unipotent elements of non-prime order in irreducible representations of the exceptional algebraic groups in good characteristics are found. It is proved that if p > 5 for a group of type E-8 and ...
2019Generalized Norm-compatible Systems on Unitary Shimura Varieties
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 ...
EPFL2019Orders that are étale-locally isomorphic
Eva Bayer Fluckiger, Mathieu Huruguen
Let R be a semilocal Dedekind domain with fraction field F. It is shown that two hereditary R-orders in central simple F-algebras that become isomorphic after tensoring with F and with some faithfully flat étale R-algebra are isomorphic. On the other hand, ...
2019Reductive overgroups of distinguished unipotent elements in simple algebraic groups
Let be a simple linear algebraic group over an algebraically closed field of characteristic . In this thesis, we investigate closed connected reductive subgroups that contain a given distinguished unipotent element of . Our ...
EPFL2018Irreducible representations of simple algebraic groups in which a unipotent element is represented by a matrix with a single non-trivial Jordan block
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 ...
2018On 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 Heidelberg2017Invariant forms on irreducible modules of simple algebraic groups
Let G be a simple linear algebraic group over an algebraically dosed field K of characteristic p >= 0 and let V be an irreducible rational G-module with highest weight A. When is self-dual, a basic question to ask is whether V has a non-degenerate G-invari ...
Elsevier2017Special Reductive Groups Over An Arbitrary Field
A linear algebraic group G defined over a field k is called special if every G-torsor over every field extension of k is trivial. In 1958 Grothendieck classified special groups in the case where the base field is algebraically closed. In this paper we desc ...
Springer Birkhauser2016