Variations on themes of Kostant

Details Variations on themes of Kostant Variations on themes of Kostant

2007-10-08

arxiv.org/abs/0710.1443v2

Mathematics

Representation Theory

Final version to appear in a special volume dedicated to Bertram Kostant. It supercedes arXiv:math.AG/9803141

Scientific paper

Let g be a complex semisimple Lie algebra and let G' be the Langlands dual group. We give a description of the cohomology algebra of an arbitrary spherical Schubert variety in the loop Grassmannian for G' as a quotient of the form Sym(g^e)/J. Here, J is an appropriate ideal in the symmetric algebra of g^e, the centralizer of a principal nilpotent in g. We also discuss a `topological' proof of Kostant's famous result on the structure of the polynomial algebra on g.

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