1. Cohomology of the minimal nilpotent orbit
- Author
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Daniel Juteau, Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU), Laboratoire de Mathématiques Nicolas Oresme ( LMNO ), Université de Caen Normandie ( UNICAEN ), and Normandie Université ( NU ) -Normandie Université ( NU ) -Centre National de la Recherche Scientifique ( CNRS )
- Subjects
Fundamental group ,Pure mathematics ,correspondance de Springer ,20G99 ,Nilpotent orbit ,[ MATH.MATH-AT ] Mathematics [math]/Algebraic Topology [math.AT] ,01 natural sciences ,Mathematics::Algebraic Topology ,symbols.namesake ,Mathematics::K-Theory and Homology ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,0103 physical sciences ,Lie algebra ,FOS: Mathematics ,Trivial representation ,Representation Theory (math.RT) ,0101 mathematics ,Mathematics ,Weyl group ,Algebra and Number Theory ,Chern class ,systèmes de racines ,[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT] ,010102 general mathematics ,calcul de Schubert ,Cohomology ,[ MATH.MATH-RT ] Mathematics [math]/Representation Theory [math.RT] ,[MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT] ,Torsion (algebra) ,symbols ,Cohomologie entière ,orbite nilpotente minimale ,010307 mathematical physics ,Geometry and Topology ,suite de Gysin ,Mathematics - Representation Theory - Abstract
We compute the integral cohomology of the minimal non-trivial nilpotent orbit in a complex simple (or quasi-simple) Lie algebra. We find by a uniform approach that the middle cohomology group is isomorphic to the fundamental group of the sub-root system generated by the long simple roots. The modulo $\ell$ reduction of the Springer correspondent representation involves the sign representation exactly when $\ell$ divides the order of this cohomology group. The primes dividing the torsion of the rest of the cohomology are bad primes., 29 pages, v2 : Leray-Serre spectral sequence replaced by Gysin sequence only, corrected typos
- Published
- 2008
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