Some Pieri-type formulas for flag manifolds
	Algebraic Geometry Seminar
	University of Chicago
	18 February 1998

	Frank Sottile
	University of Toronto


The Chow rings of flag varieties G/B have integral bases of Schubert
classes, S_w for w in the Weyl group of G.  Thus there exist (nonnegative)
integral constants c^w_{u v} defined by the identity

S_u S_v = \sum_w c^w_{u v} S_w

These generalize the Littlewood-Richardson coefficients and are expected to
have rich combinatorial properties.  Much is known about these rings,
including presentations, formulas for the Schubert classes, and how to
multiply a Schubert class by a generator.  It however remains an open
problem to say anything meaningful about these c^w_{u v}.

In this talk, we will discuss some of what is known about these c^w_{u v}.
We concentrate on Pieri-type formulas, that is, when S_v is a special
Schubert class.  Our goal is to describe how geometry has helped shed light
on these (apparently) purely combinatorial questions.