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Simple Stationary Steps in Quantum Walks

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dc.contributor.authorShaplin, Richard Martinen
dc.contributor.committeechairOrr, Daniel D.en
dc.contributor.committeememberShimozono, Mark M.en
dc.contributor.committeememberMihalcea, Constantin Leonardoen
dc.contributor.committeememberLoehr, Nicholas A.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2024-05-08T08:01:15Zen
dc.date.available2024-05-08T08:01:15Zen
dc.date.issued2024-05-07en
dc.description.abstractThe inverse Chevalley formula in the equivariant K-theory of semi-infinite flag manifolds of type An−1 is given as a sum over a set of quantum walks in the quantum Bruhat graph, QBG(An−1). We establish bounds on the number of quantum steps and simple stationary steps in these quantum walks. By a result of Kato, we map this formula to the equivariant quantum K-theory of partial flag manifolds G/P to give an alternate proof of [KLNS24, Theorem 8].en
dc.description.abstractgeneralThe quantum Bruhat graph, is a directed graph with vertex set W . Beginning with an arbitrary element of W , at each position, we may either move to a new element of W along a directed edge (a non-stationary step), or stay at the current element (a stationary step). A quantum walk is the sequence that records the element W at each position. We establish bounds on the number of occurrences of particular kinds of stationary and non-stationary steps called simple stationary steps and quantum steps respectively. These bounds are relevant to calculations of Chevalley formulas in K-Theory.en
dc.description.degreeDoctor of Philosophyen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:40590en
dc.identifier.urihttps://hdl.handle.net/10919/118915en
dc.language.isoenen
dc.publisherVirginia Techen
dc.rightsCreative Commons Attribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.subjectQuantum Walksen
dc.subjectK-Theoryen
dc.titleSimple Stationary Steps in Quantum Walksen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.nameDoctor of Philosophyen

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