English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
 
 
DownloadE-Mail
 DetailsSummary
  Applying parabolic Peterson: affine algebras and the quantum cohomology of the Grassmannian

Cookmeyer, J., & Milićević, E. (2019). Applying parabolic Peterson: affine algebras and the quantum cohomology of the Grassmannian. Journal of Combinatorics, 10(1), 129-162. doi:10.4310/JOC.2019.v10.n1.a6.

Item is

 

show all hide all

Basic

show hide
Item Permalink: https://hdl.handle.net/21.11116/0000-0003-D8FC-E Version Permalink: https://hdl.handle.net/21.11116/0000-0004-738E-B
Genre: Journal Article

Files

show Files
hide Files
:
arXiv:1707.02178.pdf (Preprint), 901KB
 
File Permalink:
-
Name:
arXiv:1707.02178.pdf
Description:
File downloaded from arXiv at 2019-06-25 10:40
OA-Status:
Visibility:
Private
MIME-Type / Checksum:
application/pdf
Technical Metadata:
Copyright Date:
-
Copyright Info:
-
License:
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
:
Cookmeyer-Milicevic_Applying parabolic Peterson_2019.pdf (Publisher version), 2MB
 
File Permalink:
-
Name:
Cookmeyer-Milicevic_Applying parabolic Peterson_2019.pdf
Description:
-
OA-Status:
Visibility:
Private
MIME-Type / Checksum:
application/pdf
Technical Metadata:
Copyright Date:
-
Copyright Info:
... the authors (and their employers) retain the right to reproduce their work for “fair use” under copyright law, which precludes any profit-making use of the work. Webseite der Zeitschrift (07.08.2019) https://intlpress.com/site/pub/pages/journals/items/joc/_home/submissions/index.html
License:
-

Locators

show
hide
Locator:
http://dx.doi.org/10.4310/JOC.2019.v10.n1.a6 (Publisher version)
Description:
-
OA-Status:
Not specified

Creators

show
hide
 Creators:
Cookmeyer, Jonathan, Author
Milićević, Elizabeth1, Author           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

Content

show
hide
Free keywords: Mathematics, Combinatorics, Algebraic Geometry
 Abstract: The Peterson isomorphism relates the homology of the affine Grassmannian to the quantum cohomology of any flag variety. In the case of a partial flag, Peterson’s map is only a surjection, and one needs to quotient by a suitable ideal on the affine side to map isomorphically onto the quantum cohomology. We provide a detailed exposition of this parabolic Peterson isomorphism in the case of the Grassmannian of m-planes in complex n-space, including an explicit recipe for doing quantum Schubert calculus in terms of the appropriate subset of non-commutative k-Schur functions. As an application, we recast Postnikov’s affine approach to the quantum cohomology of the Grassmannian as a consequence of parabolic Peterson by showing that the affine nilTemperley–Lieb algebra arises naturally when forming the requisite quotient of the homology of the affine Grassmannian.

Details

show
hide
Language(s): eng - English
 Dates: 2019
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 1707.02178
URI: http://arxiv.org/abs/1707.02178
DOI: 10.4310/JOC.2019.v10.n1.a6
 Degree: -

Event

show

Legal Case

show

Project information

show

Source 1

show
hide
Title: Journal of Combinatorics
  Abbreviation : J. Comb.
Source Genre: Journal
 Creator(s):
Affiliations:
Publ. Info: International Press
Pages: - Volume / Issue: 10 (1) Sequence Number: - Start / End Page: 129 - 162 Identifier: -