Totally positive Toeplitz matrices and quantum cohomology of partial flag varieties

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dc.creatorRietsch, Konstanze
dc.date2001-12-03
dc.date.accessioned2026-07-07T04:44:57Z
dc.date.available2026-07-07T04:44:57Z
dc.descriptionWe show that the set of totally positive unipotent lower-triangular Toeplitz matrices in $GL_n$ form a real semi-algebraic cell of dimension $n-1$. Furthermore we prove a natural cell decomposition for its closure. The proof uses properties of the quantum cohomology rings of the partial flag varieties of $GL_n(\C)$ relying in particular on the positivity of the structure constants, which are enumerative Gromov--Witten invariants. We also give a characterization of total positivity for Toeplitz matrices in terms of the (quantum) Schubert classes. This work builds on some results of Dale Peterson's which we explain with proofs in the type $A$ case.
dc.identifierhttps://arxiv.org/abs/math/0112024
dc.identifierhttp://arxiv.org/abs/math/0112024
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62803
dc.subjectQuantum Algebra
dc.subjectAlgebraic Geometry
dc.subjectCombinatorics
dc.subject20G20, 15A48, 14N35, 14N15
dc.titleTotally positive Toeplitz matrices and quantum cohomology of partial flag varieties
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