Trace functions on Iwahori-Hecke algebras

Meinolf Geck

Banach Center Publications (1998)

  • Volume: 42, Issue: 1, page 87-109
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Geck, Meinolf. "Trace functions on Iwahori-Hecke algebras." Banach Center Publications 42.1 (1998): 87-109. <http://eudml.org/doc/208828>.

@article{Geck1998,
abstract = {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.},
author = {Geck, Meinolf},
journal = {Banach Center Publications},
keywords = {Markov trace},
language = {eng},
number = {1},
pages = {87-109},
title = {Trace functions on Iwahori-Hecke algebras},
url = {http://eudml.org/doc/208828},
volume = {42},
year = {1998},
}

TY - JOUR
AU - Geck, Meinolf
TI - Trace functions on Iwahori-Hecke algebras
JO - Banach Center Publications
PY - 1998
VL - 42
IS - 1
SP - 87
EP - 109
AB - 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.
LA - eng
KW - Markov trace
UR - http://eudml.org/doc/208828
ER -

References

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  1. [Bi] J. Birman, New points of view in knot theory, Bull. Amer. Math. Soc. 28 (1993), 253-287. Zbl0785.57001
  2. [Bo] N. Bourbaki, Groupes et algèbres de Lie, Chap. IV, V, VI, Hermann, Paris, 1968. 
  3. [BS] E. Brieskorn and K. Saito, Artin-Gruppen und Coxeter-Gruppen, Invent. Math. 17 (1972), 245-271. 
  4. [Ca] R.W. Carter, Conjugacy classes in the Weyl group, Compositio Math. 25 (1972), 1-59. Zbl0254.17005
  5. [CR] C.W. Curtis and I. Reiner, Methods of representation theory, Vol. 2, Wiley, 1987. 
  6. [Di] T. tom Dieck, Knotentheorien und Wurzelsysteme, Teil II, preprint, Math. Gottingensis 44, 1993. 
  7. [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. Zbl0872.57012
  8. [GP] M. Geck and G. Pfeiffer, On the irreducible characters of Hecke algebras, Advances in Math. 102 (1993), 79-94. Zbl0816.20034
  9. [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. Zbl0868.20013
  10. [Jo] V.F.R. Jones, Hecke algebra representations of braid groups and link polynomials, Annals Math. 126 (1987), 335-388. Zbl0631.57005
  11. [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. Zbl0884.57004
  12. [Pf] G. Pfeiffer, Charakterwerte von Iwahori-Hecke-Algebren von klassischem Typ, Aachener Beiträge zur Mathematik 14, Verlag der Augustinus-Buchhandlung, Aachen, 1995. 

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