Skip to main content

Part of the book series: Graduate Texts in Mathematics ((GTM,volume 231))

  • 5123 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

  1. S. Billey, V. Lakshmibai, Singular Loci of Schubert Varieties, Progress in Mathematics, 182, Birkhäuser Boston Inc., Boston, MA, 2000, xii+251. [24, 171]

    MATH  Google Scholar 

  2. N. Bourbaki, Groupes et algébres de Lie, Ch. 4–6, Éléments de Mathématique, Fasc. XXXIV, Hermann, Paris, 1968; Masson, Paris, 1981. [24, 88, 127, 129, 130, 170]

    MATH  Google Scholar 

  3. K. S. Brown, Buildings, Springer, New York, 1989. [24, 88]

    MATH  Google Scholar 

  4. R. W. Carter, Simple Groups of Lie Type, J. Wiley & Sons, London, 1972. [24]

    MATH  Google Scholar 

  5. R. W. Carter, Finite Groups of Lie Type: Conjugacy Classes and Complex Characters, Wiley Interscience, London, 1985. [24]

    MATH  Google Scholar 

  6. H. S. M. Coxeter, Discrete groups generated by reflections, Ann. Math. 35 (1934), 588–621. [24]

    Article  MATH  MathSciNet  Google Scholar 

  7. H. S. M. Coxeter, The complete enumeration of finite groups of the form R2i = (RiRj)kij = 1, J. London Math. Soc. 10 (1935), 21–25. [24]

    MATH  Google Scholar 

  8. H. S. M. Coxeter, W. O. J. Moser, Generators and Relations for Discrete Groups, 4th revised ed., Ergebnisse der Mathematik und ihrer Grenzgebiete 14, Springer-Verlag, Berlin, 1980. [24]

    Google Scholar 

  9. V. V. Deodhar, Some characterizations of Coxeter groups, Enseign. Math. 32 (1986), 111–120. [25]

    MATH  MathSciNet  Google Scholar 

  10. V. V. Deodhar, A note on subgroups generated by reflections in Coxeter groups, Arch. Math. 53 (1989), 543–546. [25]

    Article  MATH  MathSciNet  Google Scholar 

  11. M. J. Dyer, Reflection subgroups of Coxeter systems, J. Algebra 135 (1990), 57–73. [25]

    Article  MATH  MathSciNet  Google Scholar 

  12. W. Fulton, Young tableaux. With Applications to Representation Theory and Geometry. London Mathematical Society Student Texts 35, Cambridge University Press, Cambridge, 1997. [24, 234, 307]

    MATH  Google Scholar 

  13. M. Geck, G. Pfeiffer, On the irreducible characters of Hecke algebras, Adv. Math. 102 (1993), 79–94. [25]

    Article  MathSciNet  MATH  Google Scholar 

  14. R. Gill, On posets from conjugacy classes of Coxeter groups, Discrete Math. 216 (2000), 139–152. [25]

    Article  MATH  MathSciNet  Google Scholar 

  15. M. Hazewinkel, W. Hesselink, D. Siersma, F. D. Veldkamp, The ubiquity of Coxeter-Dynkin diagrams (an introduction to the A-D-E problem), Nieuw Arch. Wisk. 25 (1977), 257–307. [24]

    MathSciNet  MATH  Google Scholar 

  16. H. L. Hiller, Geometry of Coxeter groups, Pitman, Boston, 1982. [24, 208]

    MATH  Google Scholar 

  17. J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer, New York, 1972. [24]

    MATH  Google Scholar 

  18. J. E. Humphreys, Linear Algebraic Groups, Springer, New York, 1975. [24]

    MATH  Google Scholar 

  19. J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge University Press, Cambridge, 1990. [4, 24, 123, 124, 126, 130, 132, 134, 136, 174, 175, 200, 205, 240]

    MATH  Google Scholar 

  20. V. G. Kac, Infinite-Dimensional Lie Algebras, 3rd ed., Cambridge University Press, Cambridge, 1990. [24]

    MATH  Google Scholar 

  21. S. Kumar, Kac-Moody Groups, Their Flag Varieties and Representation Theory, Progress in Mathematics, 204, Birkhäuser, Boston, MA, 2002. [24]

    MATH  Google Scholar 

  22. H. Matsumoto, Générateurs et relations des groupes de Weyl généralisés, C.R. Acad. Sci. Paris 258 (1964), 3419–3422. [25]

    MATH  MathSciNet  Google Scholar 

  23. P. McMullen, E. Schulte, Abstract Regular Polytopes, Encyclopedia of Mathematics and its Applications, 92, Cambridge University Press, Cambridge 2002. [24]

    MATH  Google Scholar 

  24. J. Stillwell, Classical Topology and Combinatorial Group Theory, 2nd ed., Graduate Texts in Mathematics, 72. Springer-Verlag, New York, 1993. [24]

    MATH  Google Scholar 

  25. J. Stillwell, Classical Topology and Combinatorial Group Theory, 2nd ed., Graduate Texts in Mathematics, 72. Springer-Verlag, New York, 1993. [24] p 45

    MATH  Google Scholar 

  26. J. Tits, Groupes et géométries de Coxeter, preprint, I.H.E.S., Paris, 1961. [24]

    Google Scholar 

  27. J. Tits, Buildings of Spherical Type and Finite BN-pairs, Lecture Notes in Math. No. 386, Springer, Berlin, 1974. [24, 88]

    MATH  Google Scholar 

  28. D.-N. Verma, A strengthening of the exchange property of Coxeter groups, preprint, 1972. [24]

    Google Scholar 

  29. E. B. Vinberg, Discrete reflection groups in Lobachevsky spaces, Proc. Intern. Congress Math. (Warsaw, 1983), PWN, Warsaw, 1984, pp. 593–601. [24]

    Google Scholar 

  30. E. B. Vinberg, Hyperbolic reflection groups, Russian Math. Surveys 40 (1985), 31–75. [24]

    Article  MATH  MathSciNet  Google Scholar 

  31. E. Witt, Spiegelungsgruppen und Aufzählung halbeinfacher Liescher Ringe, Abh. Math. Sem. Univ. Hamburg 14 (1941), 289–322. [24]

    Article  MATH  MathSciNet  Google Scholar 

Download references

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer Science+Business Media, Inc.

About this chapter

Cite this chapter

(2005). The basics. In: Combinatorics of Coxeter Groups. Graduate Texts in Mathematics, vol 231. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27596-7_1

Download citation

Publish with us

Policies and ethics