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

Lugo, Michael Ruben2019-05-102019-05-102019-05-09vt_gsexam:19683http://hdl.handle.net/10919/89477For 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.ETDIn Copyrightcombinatoricsaffine Weyl groupaffine Grassmannianquantum Bruhat graphMöbius functioninfinite affine Weyl groupA Combinatorially Explicit Relative Möbius Function on Affine Grassmannians and a Proposal for an Affine Infinite Symmetric GroupDissertation