Low-Dimensional Unitary Representations of B_3
| dc.creator | Tuba, Imre | |
| dc.date | 1999-08-20 | |
| dc.date | 1999-12-01 | |
| dc.date.accessioned | 2026-07-07T05:30:25Z | |
| dc.date.available | 2026-07-07T05:30:25Z | |
| dc.description | We characterize all simple unitarizable representations of the braid group $B_3$ on complex vector spaces of dimension $d \leq 5$. In particular, we prove that if $σ_1$ and $σ_2$ denote the two generating twists of $B_3$, then a simple representation $ρ:B_3 \to \gl(V)$ (for $\dim V \leq 5$) is unitarizable if and only if the eigenvalues $λ_1, λ_2, ..., λ_d$ of $ρ(σ_1)$ are distinct, satisfy $|λ_i|=1$ and $μ^{(d)}_{1i} > 0$ for $2 \leq i \leq d$, where the $μ^{(d)}_{1i}$ are functions of the eigenvalues, explicitly described in this paper. | |
| dc.description | Added sections + some minor updates | |
| dc.identifier | https://arxiv.org/abs/math/9908110 | |
| dc.identifier | http://arxiv.org/abs/math/9908110 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78987 | |
| dc.subject | Representation Theory | |
| dc.subject | Rings and Algebras | |
| dc.subject | 20F36, 20C07, 81R10 (Primary), 20H20, 16S34 (Secondary) | |
| dc.title | Low-Dimensional Unitary Representations of B_3 | |
| dc.type | text |