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Poset Pinball, the Dimension Pair Algorithm, and Type A Regular Nilpotent Hessenberg Varieties
Joint Authors
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-34, 34 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-06-10
Country of Publication
Egypt
No. of Pages
34
Main Subjects
Abstract EN
We develop the theory of poset pinball, a combinatorial game introduced by Harada-Tymoczko to study the equivariant cohomology ring of a GKM-compatible subspace X of a GKM space; Harada and Tymoczko also prove that, in certain circumstances, a successful outcome of Betti poset pinball yields a module basis for the equivariant cohomology ring of X.
First we define the dimension pair algorithm, which yields a successful outcome of Betti poset pinball for any type A regular nilpotent Hessenberg and any type A nilpotent Springer variety, considered as GKM-compatible subspaces of the flag variety.
The algorithm is motivated by a correspondence between Hessenberg affine cells and certain Schubert polynomials which we learned from Insko.
Second, in a special case of regular nilpotent Hessenberg varieties, we prove that our pinball outcome is poset-upper-triangular, and hence the corresponding classes form a HS1*(pt)-module basis for the S1-equivariant cohomology ring of the Hessenberg variety.
American Psychological Association (APA)
Bayegan, Darius& Harada, Megumi. 2012. Poset Pinball, the Dimension Pair Algorithm, and Type A Regular Nilpotent Hessenberg Varieties. ISRN Geometry،Vol. 2012, no. 2012, pp.1-34.
https://search.emarefa.net/detail/BIM-457741
Modern Language Association (MLA)
Bayegan, Darius& Harada, Megumi. Poset Pinball, the Dimension Pair Algorithm, and Type A Regular Nilpotent Hessenberg Varieties. ISRN Geometry No. 2012 (2012), pp.1-34.
https://search.emarefa.net/detail/BIM-457741
American Medical Association (AMA)
Bayegan, Darius& Harada, Megumi. Poset Pinball, the Dimension Pair Algorithm, and Type A Regular Nilpotent Hessenberg Varieties. ISRN Geometry. 2012. Vol. 2012, no. 2012, pp.1-34.
https://search.emarefa.net/detail/BIM-457741
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-457741