English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Maximal Newton points and the quantum Bruhat graph

MPS-Authors
/persons/resource/persons239260

Milićević,  Elizabeth
Max Planck Institute for Mathematics, Max Planck Society;

External Resource
Fulltext (public)

1606.07478.pdf
(Preprint), 2MB

Supplementary Material (public)
There is no public supplementary material available
Citation

Milićević, E. (2021). Maximal Newton points and the quantum Bruhat graph. Michigan Mathematical Journal, 70(3), 451-502. doi:10.1307/mmj/20175356.


Cite as: http://hdl.handle.net/21.11116/0000-0007-ADB3-C
Abstract
We discuss a surprising relationship between the partially ordered set of Newton points associated with an affine Schubert cell and the quantum cohomology of the complex flag variety. The main theorem provides a combinatorial formula for the unique maximum element in this poset in terms of paths in the quantum Bruhat graph, whose vertices are indexed by elements in the finite Weyl group. Key to establishing this connection is the fact that paths in the quantum Bruhat graph encode saturated chains in the strong Bruhat order on the affine Weyl group. This correspondence is also fundamental in the work of Lam and Shimozono establishing Peterson’s isomorphism between the quantum cohomology of the finite flag variety and the homology of the affine Grassmannian. One important geometric application of the present work is an inequality which provides a necessary condition for nonemptiness of certain affine Deligne–Lusztig varieties in the affine flag variety.