A Combinatorially Explicit Relative Möbius Function on Affine Grassmannians and a Proposal for an Affine Infinite Symmetric Group

For an affine Weyl group W, we explicitly determine the elements for which the Möbius function of the subposet of affine Grassmannians under the Bruhat order is non-zero by utilizing the quantum Bruhat graph of the classical Weyl group associated to W . Then we examine embedding stable and consistent statistics on the affine Weyl group of type A which permit the definition of an affine infinite symmetric group.

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 dc:creator

• Lugo, Michael Ruben

Chair dc:contributor.committeechair

• Shimozono, Mark M.

Committee members dc:contributor.committeemember

• Orr, Daniel D.
• Mihalcea, Constantin Leonardo
• Loehr, Nicholas A.

• combinatorics
• affine Weyl group
• affine Grassmannian
• quantum Bruhat graph
• Möbius function
• infinite affine Weyl group

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:19683

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/89477