A Chevalley-Monk and Giambelli’s Formula for Peterson Varieties of All Lie Types
نویسنده
چکیده
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 acting on it. We give a basis of Peterson Schubert classes for H∗ S1(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 ChevalleyMonk rule and Giambelli’s formula for all Lie types. Résumé. Une variété de Peterson est une sous-variété de G/B qui provient de la construction de la cohomologie quantique des variétés de drapeaux partielles. Chacune a un tore d’une dimension, S qui y agit. Nous présentons une base des classes de Peterson Schubert pour H∗ S1(Pet) et identifions les générateurs de l’anneau. Harada-Tymoczko ont fourni une formule de Monk positive pour le type A, et Bayegan-Harada ont donné une formule Giambelli pour multiplication dans l’anneau de la cohomologie. Cet article donne une règle Chevalley-Monk et une formule de Giambelli dans tous les types de Lie.
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