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Decomposition Varieties in Semisimple Lie Algebras

Published online by Cambridge University Press:  20 November 2018

Abraham Broer
Abraham Broer*
Affiliation:
Département de mathématiques et de statistique Université de Montréal C.P. 6128, succursale Centre-ville Montréal, Québec H3C 3J7 email: broera@DMS.UMontreal.CA
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Abstract

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The notion of decompositon class in a semisimple Lie algebra is a common generalization of nilpotent orbits and the set of regular semisimple elements.We prove that the closure of a decomposition class has many properties in common with nilpotent varieties, e.g., its normalization has rational singularities.

The famous Grothendieck simultaneous resolution is related to the decomposition class of regular semisimple elements. We study the properties of the analogous commutative diagrams associated to an arbitrary decomposition class.

Keywords

14L3014M1715A3017B45
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 50 , Issue 5 , 01 October 1998 , pp. 929 - 971
Copyright
Copyright © Canadian Mathematical Society 1998

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