Simple Stationary Steps in Quantum Walks
| dc.contributor.author | Shaplin III, Richard Martin | en |
| dc.contributor.committeechair | Orr, Daniel D. | en |
| dc.contributor.committeemember | Shimozono, Mark M. | en |
| dc.contributor.committeemember | Mihalcea, Constantin Leonardo | en |
| dc.contributor.committeemember | Loehr, Nicholas A. | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessioned | 2024-05-08T08:01:15Z | en |
| dc.date.available | 2024-05-08T08:01:15Z | en |
| dc.date.issued | 2024-05-07 | en |
| dc.description.abstract | The 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.abstractgeneral | The 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.degree | Doctor of Philosophy | en |
| dc.format.medium | ETD | en |
| dc.identifier.other | vt_gsexam:40590 | en |
| dc.identifier.uri | https://hdl.handle.net/10919/118915 | en |
| dc.language.iso | en | en |
| dc.publisher | Virginia Tech | en |
| dc.rights | Creative Commons Attribution 4.0 International | en |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | en |
| dc.subject | Quantum Walks | en |
| dc.subject | K-Theory | en |
| dc.title | Simple Stationary Steps in Quantum Walks | en |
| dc.type | Dissertation | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | doctoral | en |
| thesis.degree.name | Doctor of Philosophy | en |
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