Quantum cohomology of flag manifolds G/B and quantum Toda lattices
Bumsig Kim
TL;DR
This paper proves the Givental conjecture linking the quantum cohomology of flag manifolds to Toda lattice conservation laws and uncovers the quantum differential module structure of these manifolds.
Contribution
It establishes the connection between quantum cohomology of flag manifolds and Toda lattices and describes their quantum differential module structure.
Findings
Quantum cohomology of G/B is governed by Toda lattice conservation laws
Quantum differential module structure of flag manifolds is characterized
Givental conjecture is proven for equivariant quantum cohomology
Abstract
We prove the Givental conjecture that the (equivariant) quantum cohomology of flag manifolds G/B are governed by the conservation law of Toda lattices. In addition, we find the quantum differential module structure of the flag manifolds.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Advanced Algebra and Geometry