Exceptional representations of simple algebraic groups - Guerreiro, Marinês
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Let G be a simply connected simple algebraic group over an algebraically closed field K of positive characteristic p, with root system R and g=L(G) be its restricted Lie algebra. Let V be a finite dimensional g-module over K. For any point v in V, the isotropy subgroup of v in G and the isotropy subalgebra of v in g are defined. A restricted g-module V is called exceptional if for each v in V, its isotropy subalgebra contains a non-central element. This book presents a classification of irreducible exceptional g-modules. A necessary condition for a g-module to be exceptional is found and a…mehr

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Produktbeschreibung
Let G be a simply connected simple algebraic group over an algebraically closed field K of positive characteristic p, with root system R and g=L(G) be its restricted Lie algebra. Let V be a finite dimensional g-module over K. For any point v in V, the isotropy subgroup of v in G and the isotropy subalgebra of v in g are defined. A restricted g-module V is called exceptional if for each v in V, its isotropy subalgebra contains a non-central element. This book presents a classification of irreducible exceptional g-modules. A necessary condition for a g-module to be exceptional is found and a complete classification of modules over groups of simple algebraic groups of exceptional type and of classical type A is obtained. For modules over groups of classical types B, C and D, the general problem is reduced to a short list of unclassified modules. The classification of exceptional modules is expected to have applications in modular invariant theory and in the classification of modularsimple Lie superalgebras.
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Autorenporträt
Marinês Guerreiro is Professor at Federal University of Viçosa (Brazil), has a Teaching Degree in Mathematics (UFSM-1988), M.Sc. in Mathematics (UnB-1991) and Ph.D. in Mathematics (University of Manchester-1997). Her research interests are Representation Theory of Groups and Lie algebras and applications of Algebra to Information and Coding Theory.