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Entanglement Theory Quantum Correlations
Open Quantum Systems Decoherence
Topological Quantum Computing
Quantum Simulation
Chevalley-Monk and Giambelli formulas for Peterson Varieties
DOAJ
Authors: Elizabeth Drellich
Year
2014
Paper ID
38818
Status
Peer-reviewed
Abstract Read
~2 min
Abstract Words
99
Citations
N/A
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 S1 acting on it. We give a basis of Peterson Schubert classes for HS1^*(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.
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- This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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- A Peterson variety is a subvariety of the flag variety G/B defined by certain linear conditions.
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