Browsing Department of Pure Mathematics and Mathematical Statistics (DPMMS) by Subject "Representation theory"
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On eigenvectors for semisimple elements in actions of algebraic groups
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 20100209)Let $G$ be a simple simply connected algebraic group defined over an algebraically closed field $K$ and $V$ an irreducible module defined over $K$ on which $G$ acts. Let $E$ denote the set of vectors in $V$ which are ...

Unipotent elements in algebraic groups
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 20120110)This thesis is concerned with three distinct, but closely related, research topics focusing on the unipotent elements of a connected reductive algebraic group G, over an algebraically closed field k, and nilpotent elements ...