On Fusion Algebras and Modular Matrices
| dc.creator | Gannon, T. | |
| dc.creator | Walton, M. A. | |
| dc.date | 1997-09-26 | |
| dc.date.accessioned | 2026-07-07T11:36:46Z | |
| dc.date.available | 2026-07-07T11:36:46Z | |
| dc.description | We consider the fusion algebras arising in e.g. Wess-Zumino-Witten conformal field theories, affine Kac-Moody algebras at positive integer level, and quantum groups at roots of unity. Using properties of the modular matrix $S$, we find small sets of primary fields (equivalently, sets of highest weights) which can be identified with the variables of a polynomial realization of the $A_r$ fusion algebra at level $k$. We prove that for many choices of rank $r$ and level $k$, the number of these variables is the minimum possible, and we conjecture that it is in fact minimal for most $r$ and $k$. We also find new, systematic sources of zeros in the modular matrix $S$. In addition, we obtain a formula relating the entries of $S$ at fixed points, to entries of $S$ at smaller ranks and levels. Finally, we identify the number fields generated over the rationals by the entries of $S$, and by the fusion (Verlinde) eigenvalues. | |
| dc.description | 28 pages, plain TeX | |
| dc.identifier | https://arxiv.org/abs/q-alg/9709039 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9709039 | |
| dc.identifier | Commun.Math.Phys.206:1-22,1999 | |
| dc.identifier | doi:10.1007/s002200050695 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/199034 | |
| dc.subject | Quantum Algebra | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | On Fusion Algebras and Modular Matrices | |
| dc.type | text |