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GROMOV–WITTEN INVARIANTS OF FLAG MANIFOLDS, VIA D-MODULES

Published online by Cambridge University Press:  20 July 2005

A. AMARZAYA  and
M. A. GUEST
A. AMARZAYA
Affiliation:
Department of Mathematics, Graduate School of Science, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji-shi, Tokyo 192-0397, Japan Current address: School of Mathematics and Computer Science, National University of Mongolia, Ulannbaatar, Post Box 586, Post Office 46-A, Mongolia
M. A. GUEST
Affiliation:
Department of Mathematics, Graduate School of Science, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji-shi, Tokyo 192-0397, Japan
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Abstract

We present a method for computing the 3-point genus zero Gromov–Witten invariants of the complex flag manifold $G/B$ from the relations of the small quantum cohomology algebra $QH^\ast G/B$ ($G$ is a complex semisimple Lie group and $B$ is a Borel subgroup). In [3] and [9], at least in the case $G={\rm GL}_n{\bf C}$, two algebraic/combinatoric methods have been proposed, based on suitably designed axioms. Our method is quite different, being differential geometric in nature; it is based on the approach to quantum cohomology described in [7], which is in turn based on the integrable systems point of view of Dubrovin and Givental.

Keywords

14N35 (primary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 72 , Issue 1 , August 2005 , pp. 121 - 136
Copyright
The London Mathematical Society 2005

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