Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra
By V. Gorbounov, Richárd Rimányi, V. Tarasov, A. Varchenko. 2012
57 citations recorded by the source corpus.
Abstract We interpret the equivariant cohomology algebra H G L n × C ∗ ∗ ( T ∗ F λ ; C ) of the cotangent bundle of a partial flag variety F λ parametrizing chains of subspaces 0 = F 0 ⊂ F 1 ⊂ ⋯ ⊂ F N = C n , dim F i / F i − 1 = λ i , as the Yangian Bethe algebra B ∞ ( 1 D V λ − ) of the g l N -weight subspace 1 D V λ − of a Y ( g l N ) -module 1 D V − . Under this identification the dynamical connection of Tarasov and Varchenko (2002) [12] turns into the quantum connection of Braverman et al. (2010) [4] and Maulik and Okounkov (2012) [5] . As a result of this identification we describe the algebra of quantum multiplication on H G L n × C ∗ ∗ ( T ∗ F λ ; C ) as the algebra of functions on fibers of a discrete Wronski map. In particular this gives generators and relations of that algebra. This identification also gives us hypergeometric solutions of the associated quantum differential equation. That fact manifests the Landau–Ginzburg mirror symmetry for the cotangent bundle of the flag variety.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/41b11d17bd1e57ee2b8dfe36dd27ce3bae483ce0
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Citations in the corpus
- Shadows of characteristic cycles, Verma modules, and positivity of Chern–Schwartz–MacPherson classes of Schubert cells (2017, result): “Similar orthogonality results, in the language of weight functions were obtained in [45, 47, 49, 23], for the type A flag manifolds.”