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Homological representations of the Hecke algebra. (English) Zbl 0716.20022
Es werden Darstellungen von Hecke Algebren mit Hilfe von Monodromie- Darstellungen in einem Vektorraumbündel mit einem natürlichen flachen Zusammenhang konstruiert. Dabei sind die Fasern Homologie-Vektorräume von Konfigurationsräumen von Punkten in der komplexen Ebene, wie man sie in der Zopftheorie betrachtet. Der Ansatz führt auf eine topologische Beschreibung des Jones Polynoms, die in einem Preprint vorliegt. Die durchgeführte Konstruktion hängt eng zusammen mit A. Tsuchiya, Y. Kanie [Adv. Stud. Pure Math. 16, 297-372 (1988; Zbl 0661.17021), Erratum ibid. 19, 675-682 (1989; Zbl 0699.17019)]. Als Spezialfall ergibt sich die Burau-Darstellung der Zopfgruppe bzw. das Alexanderpolynom einer Verkettung.
Reviewer: G.Burde

MSC:
20G05 Representation theory for linear algebraic groups
17B65 Infinite-dimensional Lie (super)algebras
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
20F36 Braid groups; Artin groups
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
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