On thin irreducible T-modules with endpoint 1

Date of Publication

8-2011

Document Type

Master's Thesis

Degree Name

Master of Science in Mathematics

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics

Thesis Adviser

Arlene Pascasio

Defense Panel Chair

Ederlina Nocon

Defense Panel Member

Edmundo Perez
Melvin Vidar

Abstract/Summary

Consider a distance-regular graph Γ = (X, R) with D ≥ 3 and adjacency matrix A. The subalgebra of M atX(C) generated by A is called the Bose-Mesner algebra M of Γ. Fix a vertex x ∈ X. Let E ∗ 0 , . . . , E∗ D denote the dual primitive idempotents of Γ with respect to x. The subalgebra of M atX(C) generated by A, E∗ 0 , . . . , E∗ D is called the subconstituent algebra or Terwilliger algebra of Γ with respect to x and denoted by T. Let V = C X be the standard module of Γ with the usual Hermitian inner product. Define s1 ∈ V to be the vector with 1’s in the entries labeled by vertices adjacent to x and 0’s elsewhere. Let 0 6 = v ∈ E ∗ 1V such that hv, s1i = 0. Go and Terwilliger were able to show in [Europ. J. Combinatorics, 23, (2002),793-816] that the space Mv is of dimension D −1 or D. They then showed that Mv is a thin irreducible T-module with endpoint 1 when the dimension of Mv is D − 1. In this paper, we consider the case when Mv has dimension D, and show a necessary and sufficient condition for Mv to be a thin irreducible T-module with endpoint 1.

Abstract Format

html

Language

English

Format

Electronic

Accession Number

CDTG005006

Shelf Location

Archives, The Learning Commons, 12F Henry Sy Sr. Hall

Keywords

Irreducible polynomials

Upload Full Text

wf_yes

Embargo Period

2-13-2022

This document is currently not available here.

Share

COinS