Chevalley-Monk and Giambelli formulas for Peterson VarietiesReport as inadecuate




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1 UMass Amherst - University of Massachusetts Amherst

Abstract : A Peterson variety is a subvariety of the flag variety $G-B$ defined by certain linear conditions. Peterson varieties appear in the construction of the quantum cohomology of partial flag varieties and in applications to the Toda flows. Each Peterson variety has a one-dimensional torus $S^1$ acting on it. We give a basis of Peterson Schubert classes for $H {S^1}^*Pet$ and identify the ring generators. In type A Harada-Tymoczko gave a positive Monk formula, and Bayegan-Harada gave Giambelli-s formula for multiplication in the cohomology ring. This paper gives a Chevalley-Monk rule and Giambelli-s formula for all Lie types.

Keywords : Peterson variety Chevalley-Monk formula Giambelli-s formula equivariant cohomology





Author: Elizabeth Drellich -

Source: https://hal.archives-ouvertes.fr/



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