q-Pascal's triangle and irreducible representations of the braid group B_3 in arbitrary dimension

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dc.creatorAlbeverio, Sergio
dc.creatorKosyak, Alexandre
dc.date2008-03-19
dc.date2008-03-24
dc.date.accessioned2026-07-07T09:27:49Z
dc.date.available2026-07-07T09:27:49Z
dc.descriptionWe construct a [(n+1)/2]+1 parameters family of irreducible representations of the Braid group B_3 in arbitrary dimension n\in N, using a q-deformation of the Pascal triangle. This construction extends in particular results by S.P.Humphries [8], who constructed representations of the braid group B_3 in arbitrary dimension using the classical Pascal triangle. E.Ferrand [7] obtained an equivalent representation of B_3 by considering two special operators in the space C^n[X]. Slightly more general representations were given by I.Tuba and H.Wenzl [11]. They involve [(n+1)/2] parameters (and also use the classical Pascal triangle). The latter authors also gave the complete classification of all simple representations of B_3 for dimension n\leq 5. Our construction generalize all mentioned results and throws a new light on some of them. We also study the irreducibility and the equivalence of the representations. In [17] we establish the connection between the constructed representation of the braid group B_3 and the highest weight modules of U(sl_2) and quantum group U_q(sl_2).
dc.description64 pages
dc.identifierhttps://arxiv.org/abs/0803.2778
dc.identifierhttp://arxiv.org/abs/0803.2778
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/157242
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.subject20F36, 05A30, 11B56, 17B37
dc.titleq-Pascal's triangle and irreducible representations of the braid group B_3 in arbitrary dimension
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