Jones Pairs
| dc.creator | Chan, Ada | |
| dc.date | 2007-07-12 | |
| dc.date.accessioned | 2026-07-07T08:16:17Z | |
| dc.date.available | 2026-07-07T08:16:17Z | |
| dc.description | Motivated by Jones' braid group representations constructed from spin models, we define {\sl a Jones pair} to be a pair of $\nbyn$ matrices $(A,B)$ such that the endomorphisms $X_A$ and $\D_B$ form a representation of a braid group. When $A$ and $B$ are type-II matrices, we call $(A,B)$ {\sl an invertible Jones pair}. We develop the theory of Jones pairs in this thesis. Our aim is to study the connections among association schemes, spin models and four-weight spin models using the viewpoint of Jones pairs. We use Nomura's method to construct a pair of algebras from the matrices $(A,B)$, which we call the Nomura algebras of $(A,B)$. These algebras become the central tool in this thesis. We explore their properties in Chapters \ref{Nomura} and \ref{IINom}. In Chapter \ref{JP}, we introduce Jones pairs. We prove the equivalence of four-weight spin models and invertible Jones pairs. We extend some existing concepts for four-weight spin models to Jones pairs. In Chapter \ref{SpinModels}, we provide new proofs for some well-known results on the Bose-Mesner algebras associated with spin models. We document the main results of the thesis in Chapter \ref{InvJP}. We prove that every four-weight spin model comes from a symmetric spin model (up to odd-gauge equivalence). We present four Bose-Mesner algebras associated to each four-weight spin model. We study the relations among these algebras. In particular, we provide a strategy to search for four-weight spin models. This strategy is analogous to the method given by Bannai, Bannai and Jaeger for finding spin models. | |
| dc.description | 155 pages, Thesis | |
| dc.identifier | https://arxiv.org/abs/0707.1848 | |
| dc.identifier | http://arxiv.org/abs/0707.1848 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133729 | |
| dc.subject | Combinatorics | |
| dc.subject | 05E30 | |
| dc.title | Jones Pairs | |
| dc.type | text |