Murray State Theses and Dissertations

Abstract

One of the great themes of algebraic combinatorics is the exploration of connections between ordered structures and group actions/representations. This thesis furthers this theme by presenting diamond-colored distributive lattice models of certain poly nomials that are invariant under the action of the type Bn Weyl group. Initially we realize these lattices as diamond-colored lattices of order ideals from certain vertex colored posets. We explore various coordinatizations of these lattices via partition-like elements, tableaux, and binary-type representations called tally diagrams. We also examine algebraic properties of these lattices. In particular, we prove that our type Bn lattices are effective models for the type Bn elementary Weyl symmetric functions.

Year manuscript completed

2018

Year degree awarded

2018

Author's Keywords

integer partition, diamond-colored distributive lattice, vertex-colored poset of join irreducibles, elementary symmetric function, Weyl group symmetric function, splitting poset

Thesis Advisor

Robert G. Donnelly

Committee Chair

Robert G. Donnelly

Committee Member

Elizabeth Donovan

Committee Member

Timothy Schroeder

Document Type

Thesis

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