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Algebra Seminar
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Matthew Dyer
University of Notre Dnme

BGG operators and binomial coefficients.

Friday 25th October, 12-1pm, Carslaw 373.

In studying the cohomology ring of the flag variety of a semisimple complex algebraic group, Bernstein, Gelfand and Gelfand were led to define, purely in terms of the Weyl group and root system, certain operators on the symmetric algebra of the Cartan subalgebra. For general Coxeter groups, we shall describe some simple algebraic and combinatorial results according to which these operators are determined by corresponding operators for dihedral groups, for which they may be explicitly described using binomial coefficients modelled on sequences of root coefficients. The results have applications to the study of Schubert varieties and prime characteristic analogues of category O of modules for a semisimple complex Lie algebra.