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SUMMARY:Eigenvalue multiplicities in representations of simple algebraic g
 roups - Donna Testerman (EPFL - Ecole Polytechnique Fédérale de Lausanne
 )
DTSTART:20220509T102000Z
DTEND:20220509T105000Z
UID:TALK172763@talks.cam.ac.uk
DESCRIPTION:After a brief historical overview of the study of eigenvalue m
 ultiplicities in representations of simple algebraicgroups and the finite 
 groups of Lie type\, we report on two recent articles with A. Zalesski\, i
 n which we studysemisimple elements having &ldquo\;almost simple&rdquo\; s
 pectrum in an irreducible representation of a simple algebraicgroup. More 
 precisely\, we show that if such an element acts with at most one eigenval
 ue of multiplicitygreater than 1 in some irreducible representation of a s
 imple algebraic group\, then all nonzero weights ofthe representation have
  multiplicity one and with very few exceptions the semisimple element is r
 egular.We go on to study the behavior of regular semisimple elements actin
 g on the representations whose nonzeroweights have multiplicity 1 and intr
 oduce the notion of a &ldquo\;strongly regular&rdquo\; semisimple element 
 and showthat\, with specified exceptions\, a semisimple element acting wit
 h almost simple spectrum on some irreduciblerepresentation of a simple alg
 ebraic group is strongly regular.
LOCATION:Seminar Room 1\, Newton Institute
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