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arXiv · 0704.3417

Cohomology of the minimal nilpotent orbit

Daniel Juteau
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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.

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BibTeXRIS

Daniel Juteau. 2007-06-13. Cohomology of the minimal nilpotent orbit. https://doi.org/10.1007/s00031-008-9009-x

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