ELibM Journals • ELibM Home • EMIS Home • EMIS Mirrors

  EMIS Electronic Library of Mathematics (ELibM)
The Open Access Repository of Mathematics
  EMIS ELibM Electronic Journals

JOURNAL OF
ALGEBRAIC
COMBINATORICS

  Editors-in-chief: C. A. Athanasiadis, T. Lam, A. Munemasa, H. Van Maldeghem
ISSN 0925-9899 (print) • ISSN 1572-9192 (electronic)
 

Twisted identities in Coxeter groups

Axel Hultman
KTH Department of Mathematics 100 44 Stockholm Sweden

DOI: 10.1007/s10801-007-0106-z

Abstract

Given a Coxeter system ( W, S) equipped with an involutive automorphism  θ , the set of twisted identities is
i( q)={ q( w -1) w | w Ĩ W}. ι(θ)=\{θ(w^{-1})w\mid w\in W\}.

Pages: 313–332

Keywords: keywords Coxeter groups; Bruhat order; twisted identities; twisted involutions

Full Text: PDF

References

1. Björner, A.: Topological methods. In: Graham, R., Grötschel, M., Lovász, L. (eds.) Handbook of Combinatorics, pp. 1819-1872. North-Holland, Amsterdam (1995)
2. Björner, A., Brenti, F.: Combinatorics of Coxeter Groups. Graduate Texts in Mathematics, vol.
231. Springer, New York (2005)
3. Björner, A., Wachs, M.: Bruhat order of Coxeter groups and shellability. Adv. Math. 43, 87-100 (1982)
4. Chari, M.: On discrete Morse functions and combinatorial decompositions. Discrete Math. 217, 101- 113 (2000)
5. Deodhar, V.V.: Some characterizations of Bruhat ordering on a Coxeter group and determination of the relative Möbius function. Invent. Math. 39, 187-198 (1977)
6. Deodhar, R.S., Srinivasan, M.K.: A statistic on involutions. J. Algebr. Comb. 13, 187-198 (2001)
7. Forman, R.: Morse theory for cell complexes. Adv. Math. 134, 90-145 (1998)
8. Hée, J.-Y.: Systèmes de racines sur un anneau commutatif totalement ordonné. Geom. Dedicata 37, 65-102 (1991)
9. Hultman, A.: Fixed points of involutive automorphisms of the Bruhat order. Adv. Math. 195, 283-296 (2005) J Algebr Comb (2008) 28: 313-332
10. Hultman, A.: The combinatorics of twisted involutions in Coxeter groups. Trans. Am. Math. Soc. 359, 2787-2798 (2007)
11. Humphreys, J.E.: Reflection Groups and Coxeter Groups. Cambridge Studies in Advanced Mathematics, vol.
29. Cambridge Univ. Press, Cambridge (1990)
12. Mühlherr, B.: Coxeter groups in Coxeter groups. In: Finite Geometry and Combinatorics, Deinze,
1992. London Math. Soc. Lecture Note Ser., vol. 191, pp. 277-287. Cambridge Univ. Press, Cambridge (1993)
13. Richardson, R.W., Springer, T.A.: The Bruhat order on symmetric varieties. Geom. Dedicata 35, 389- 436 (1990)
14. Richardson, R.W., Springer, T.A.: Complements to: The Bruhat order on symmetric varieties. Geom.




© 1992–2009 Journal of Algebraic Combinatorics
© 2012 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition