Simple Stationary Steps in Quantum Walks

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].

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2024

Author dc:creator

• Shaplin, Richard Martin

Chair dc:contributor.committeechair

• Orr, Daniel D.

Committee members dc:contributor.committeemember

• Shimozono, Mark M.
• Mihalcea, Constantin Leonardo
• Loehr, Nicholas A.

• Quantum Walks
• K-Theory

Statement dc:rights

• Creative Commons Attribution 4.0 International

Licence dc:rights.uri

• http://creativecommons.org/licenses/by/4.0/

Language dc:language.iso

en

Dc Identifier Other

vt_gsexam:40590

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/118915