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Title: Positivity of Peterson Schubert calculus
Abstract. The Peterson variety is a subvariety of the flag manifold G/B equipped with an action of a one-dimensional torus, and a torus invariant paving by affine cells, called Peterson cells. We prove that the equivariant pull-backs of Schubert classes indexed by arbitrary Coxeter elements are dual (up to an intersection multiplicity) to the fundamental classes of Peterson cell closures. Dividing these classes by the intersec- tion multiplicities yields a Z-basis for the equivariant cohomology of the Peterson variety. We prove several properties of this basis, including a Graham positivity property for its structure constants, and stability with respect to inclusion in a larger Peterson variety. We also find for- mulae for intersection multiplicities with Peterson classes. This explains geometrically, in arbitrary Lie type, recent positivity statements proved in type A by Goldin and Gorbutt.  more » « less
Award ID(s):
2152312 2152294
PAR ID:
10600667
Author(s) / Creator(s):
; ;
Publisher / Repository:
Elsevier Inc
Date Published:
Journal Name:
Advances in Mathematics
Volume:
455
Issue:
C
ISSN:
0001-8708
Page Range / eLocation ID:
109879
Subject(s) / Keyword(s):
Peterson variety equivariant cohomology Schubert calculus Hessenberg varieties positivity flag manifolds
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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