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  Maximal Newton points and the quantum Bruhat graph

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

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https://doi.org/10.1307/mmj/20175356 (Publisher version)
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 Creators:
Milićević, Elizabeth1, Author              
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Algebraic Geometry, Combinatorics
 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.

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Language(s): eng - English
 Dates: 2021
 Publication Status: Published in print
 Pages: 52
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 1606.07478
DOI: 10.1307/mmj/20175356
 Degree: -

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Title: Michigan Mathematical Journal
  Abbreviation : Michigan Math. J.
Source Genre: Journal
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Publ. Info: University of Michigan ; Project Euclid
Pages: - Volume / Issue: 70 (3) Sequence Number: - Start / End Page: 451 - 502 Identifier: -