This paper is an expanded version of a talk given at the Banach Center Symposium on Knot Theory in July/August 1995. Its aim is to provide a general survey about trace functions on Iwahori-Hecke algebras associated with finite Coxeter groups. The so-called Markov traces are relevant to knot theory as they can be used to construct invariants of oriented knots and links. We present a classification of Markov traces for the classical types A, B and D.
@article{bwmeta1.element.bwnjournal-article-bcpv42i1p87bwm, author = {Geck, Meinolf}, title = {Trace functions on Iwahori-Hecke algebras}, journal = {Banach Center Publications}, volume = {43}, year = {1998}, pages = {87-109}, zbl = {0901.57016}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv42i1p87bwm} }
Geck, Meinolf. Trace functions on Iwahori-Hecke algebras. Banach Center Publications, Tome 43 (1998) pp. 87-109. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv42i1p87bwm/
[000] [Bi] J. Birman, New points of view in knot theory, Bull. Amer. Math. Soc. 28 (1993), 253-287. | Zbl 0785.57001
[001] [Bo] N. Bourbaki, Groupes et algèbres de Lie, Chap. IV, V, VI, Hermann, Paris, 1968.
[002] [BS] E. Brieskorn and K. Saito, Artin-Gruppen und Coxeter-Gruppen, Invent. Math. 17 (1972), 245-271.
[003] [Ca] R.W. Carter, Conjugacy classes in the Weyl group, Compositio Math. 25 (1972), 1-59. | Zbl 0254.17005
[004] [CR] C.W. Curtis and I. Reiner, Methods of representation theory, Vol. 2, Wiley, 1987.
[005] [Di] T. tom Dieck, Knotentheorien und Wurzelsysteme, Teil II, preprint, Math. Gottingensis 44, 1993.
[006] [GL] M. Geck and S. Lambropoulou, Markov traces and knot invariants related to Iwahori-Hecke algebras of type B, J. reine angew. Math. 482 (1997), 191-213. | Zbl 0872.57012
[007] [GP] M. Geck and G. Pfeiffer, On the irreducible characters of Hecke algebras, Advances in Math. 102 (1993), 79-94. | Zbl 0816.20034
[008] [GR] M. Geck and R. Rouquier, Centers and simple modules for Iwahori-Hecke algebras, in: Finite Reductive Groups: Related Structures and Representations, Progress in Math. 141, Birkhäuser, 1997, 251-272. | Zbl 0868.20013
[009] [Jo] V.F.R. Jones, Hecke algebra representations of braid groups and link polynomials, Annals Math. 126 (1987), 335-388. | Zbl 0631.57005
[010] [La] S. Lambropoulou, Solid torus links and Hecke algebras of B-type, in: Proceedings of the Conference on Quantum Topology, D.N. Yetter (ed.), World Scientific Press, 1994. | Zbl 0884.57004
[011] [Pf] G. Pfeiffer, Charakterwerte von Iwahori-Hecke-Algebren von klassischem Typ, Aachener Beiträge zur Mathematik 14, Verlag der Augustinus-Buchhandlung, Aachen, 1995.