Abstract
dc:description.abstractGiven a finite Weyl group W_fin with root system Phi_fin, one can create the affine Weyl group W_aff by taking the semidirect product of the translation group associated to the coroot lattice for Phi_fin, with W_fin. The double affine Weyl semigroup W can be created by using a similar semidirect product where one replaces W_fin with W_aff and the coroot lattice with the Tits cone of W_aff. We classify cocovers and covers of a given element of W with respect to the Bruhat order, specifically when W is associated to a finite root system that is irreducible and simply laced. We show two approaches: one extending the work of Lam and Shimozono, and its strengthening by Milicevic, where cocovers are characterized in the affine case using the quantum Bruhat graph of W_fin, and another, which takes a more geometrical approach by using the length difference set defined by Muthiah and Orr.
Degree
thesis:*- 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
- 2019
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Welch, Amanda Renee
- Chair dc:contributor.committeechair
-
- Orr, Daniel D.
- Committee members dc:contributor.committeemember
-
- Mihalcea, Constantin Leonardo
- Shimozono, Mark M.
- Loehr, Nicholas A.
Subjects
dc:subject × 5Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Dc Identifier Other
- vt_gsexam:19309
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/89366