QUANTUM COHOMOLOGY OF FLAG MANIFOLDS AND TODA-LATTICES

Authors
GIVENTAL A KIM B
Citation
A. Givental et B. Kim, QUANTUM COHOMOLOGY OF FLAG MANIFOLDS AND TODA-LATTICES, Communications in Mathematical Physics, 168(3), 1995, pp. 609-641
Citations number
23
Categorie Soggetti
Mathematical Method, Physical Science","Physycs, Mathematical
Journal title
Communications in Mathematical Physics → ACNP
ISSN journal
00103616
Volume
168
Issue
3
Year of publication
1995
Pages
609 - 641
Database
ISI
SICI code
0010-3616(1995)168:3<609:QCOFMA>2.0.ZU;2-B
Abstract
We discuss relations of Vafa's quantum cohomology with Floer's homolog y theory, introduce equivariant quantum cohomology, formulate some con jectures about its general properties and, on the basis of these conje ctures, compute quantum cohomology algebras of the flag manifolds. The answer turns out to coincide with the algebra of regular functions on an invariant lagrangian variety of a Toda lattice.