Cohomology of the minimal nilpotent orbit

Details Cohomology of the minimal nilpotent orbit Cohomology of the minimal nilpotent orbit

2007-04-25

arxiv.org/abs/0704.3417v2

Mathematics

Representation Theory

29 pages, v2 : Leray-Serre spectral sequence replaced by Gysin sequence only, corrected typos

Scientific paper

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.

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