Low-Dimensional Unitary Representations of B_3

dc.creatorTuba, Imre
dc.date1999-08-20
dc.date1999-12-01
dc.date.accessioned2026-07-07T05:30:25Z
dc.date.available2026-07-07T05:30:25Z
dc.descriptionWe 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.descriptionAdded sections + some minor updates
dc.identifierhttps://arxiv.org/abs/math/9908110
dc.identifierhttp://arxiv.org/abs/math/9908110
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78987
dc.subjectRepresentation Theory
dc.subjectRings and Algebras
dc.subject20F36, 20C07, 81R10 (Primary), 20H20, 16S34 (Secondary)
dc.titleLow-Dimensional Unitary Representations of B_3
dc.typetext

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