Pieri-type formulas for the classical groups

Frank Sottile
MFI Oberwolfach, 4 April 1997. 


A Pieri-type formula in the Chow (or cohomology) ring of a flag variety is a
formula expressing the product of a Schubert class by a special Schubert
class in terms of the Schubert basis.  Recently, Pragacz and Ratajski have
given such formulas in the Chow rings of all Grassmannians.  We seek
Pieri-type formulas for the flag varieties expressed in terms of chains in
the Bruhat order.

This talk will discuss joint work with Nantel Bergeron towards extending and
unifying known Pieri-type formulas.  We begin with some geometric motivation
behind this `chain-theoretic' expectation, which applies to any variety with
a cell decomposition.  Then express the Pieri-type formula for the classical
flag variety in this form.  The talk will conclude by presenting a new
Pieri-type formula for Lagrangian special Schubert classes in the Chow ring
of a symplectic flag manifold.