A Giambelli formula for the S¹-equivariant cohomology of type A Peterson varieties

2010/12/18 by Darius Bayegan, Bayegan, Darius, Megumi Harada +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Primary: 14N15 #Secondary: 55N91

paper · pdf · doi:10.48550/arxiv.1012.4053

openalex publication_date 2010/12/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The main result of this note is a Giambelli formula for the Peterson Schubert classes in the S¹-equivariant cohomology ring of a type A Peterson variety. Our results depend on the Monk formula for the equivariant structure constants for the Peterson Schubert classes derived by Harada and Tymoczko. In addition, we give proofs of two facts observed by H. Naruse: firstly, that some constants which appear in the multiplicative structure of the S¹-equivariant cohomology of Peterson varieties are Stirling numbers of the second kind, and secondly, that the Peterson Schubert classes satisfy a stability property in a sense analogous to the stability of the classical equivariant Schubert classes in the T-equivariant cohomology of the flag variety.

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• Structure constants of Peterson Schubert calculus

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