Peterson's formulas for the small Gromov-Witten invariants of
 G/P -- Chris Woodward, October 25, 2002


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I will talk about the proofs of two formulas stated by Dale
Peterson which compute the structure coefficients of the small
quantum cohomology ring of G/P.  The first is a formula for
multiplication by a divisor class, and is a simple application
of the Bott residue formula and Kleiman-Bertini in the moduli
space of stable maps.  This formula is sufficient to compute
all the small GW invariants for G/B. The second is a
replacement for functoriality: it expresses any small GW
invariant of G/P in terms of one for G/B, and can be proved by
studying the type of the Harder-Narasimhan and Jordan-Holder
filtrations of the pull-back of the tautological bundle over
G/P, under a general stable map.