
Matthew Dyer
University of Notre Dnme
BGG operators and binomial coefficients.
Friday 25th October, 121pm,
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.







