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Journal of Mathematical Sciences

, Volume 121, Issue 3, pp 2419–2436 | Cite as

q-Rook Monoid Algebras, Hecke Algebras, and Schur–Weyl Duality

  • T. Halverson
  • A. Ram
Article

Abstract

When we were at the beginnings of our careers, Sergei's support helped us to believe in our work. He generously encouraged us to publish our results on Brauer and Birman–Murakami–Wenzl algebras, results which had in part, or possibly in total, been obtained earlier by Sergei himself. He remains a great inspiration for us, both mathematically and in our memory of his kindness, modesty, generosity, and encouragement to the younger generation. Bibliography: 19 titles.

Keywords

Young Generation Weyl Duality Wenzl Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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REFERENCES

  1. 1.
    S. Ariki and K. Koike, “A Hecke algebra of (ℤ/rℤ)≀S n and construction of its irreducible representations,” Adv. Math., 106, 216–243 (1994).Google Scholar
  2. 2.
    S. Ariki, “On the semisimplicity of the Hecke algbera of (ℤ/rℤ)≀S n,” J. Algebra, 169, 216–225 (1994).Google Scholar
  3. 3.
    I. Cherednik, “A new interpretation of Gelfand-Tzetlin bases,” Duke Math. J., 54, 563–577 (1987).Google Scholar
  4. 4.
    C. Curtis and I. Reiner, Methods of Representation Theory: With Applications to Finite Groups and Orders, Vol. II, Wiley, New York (1987).Google Scholar
  5. 5.
    A. Gyoja and K. Uno, “On the semisimplicity of Hecke algebras,” J. Math. Soc. Japan, 41, 75–79 (1989).Google Scholar
  6. 6.
    T. Halverson, “Representations of the q-rook monoid,” preprint (2001).Google Scholar
  7. 7.
    P. N. Hoefsmit, “Representations of Hecke algebras of finite groups with BN-pairs of classical type,” Thesis, Univ. of British Columbia (1974).Google Scholar
  8. 8.
    I. G. Macdonald, Symmetric Functions and Hall Polynomials, 2 ed., Oxford University Press, New York (1995).Google Scholar
  9. 9.
    P. P. Martin and D. Woodcock, “On the structure of the blob algebra,” J. Algebra, 225, 957–988 (2000).Google Scholar
  10. 10.
    W. D. Munn, “Matrix representations of semigroups,” Proc. Camb. Phil. Soc., 53, 5–12 (1957).Google Scholar
  11. 11.
    W. D. Munn, “The characters of the symmetric inverse semigroup,” Proc. Camb. Phil. Soc., 53, 13–18 (1957).Google Scholar
  12. 12.
    R. Orellana and A. Ram, “Affine braids, Markov traces and the category O,” Preprint (2001).Google Scholar
  13. 13.
    A. Ram, “Skew shape representations are irreducible,” preprint (1998).Google Scholar
  14. 14.
    L. Solomon, “The Bruhat decomposition, Tits system and Iwahori ring for the monoid of matrices over a finite field,” Geom. Dedicata, 36, 15–49 (1990).Google Scholar
  15. 15.
    L. Solomon, “Representations of the rook monoid,” J. Algebra (to appear).Google Scholar
  16. 16.
    L. Solomon, “Abstract No. 900-16-169,” in: Abstracts Presented to the American Math. Soc., Vol. 16,No. 2, Spring (1995).Google Scholar
  17. 17.
    L. Solomon, “The Iwahori algebra of M n(F q), a presentation and a representation on tensor space,” Preprint (2001).Google Scholar
  18. 18.
    S. Sakamoto and T. Shoji, “Schur-Weyl reciprocity for Ariki-Koike algebras,” J. Algebra, 221, 293–314 (1999).Google Scholar
  19. 19.
    A. Young, “On quantitative substitutional analysis. VI,” Proc. London Math. Soc., 31, 253–289 (1931).Google Scholar

Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • T. Halverson
    • 1
  • A. Ram
    • 2
  1. 1.Department of Mathematics and Computer Science Macalester CollegeSt. Paul
  2. 2.Department of MathematicsUniversity of WisconsinMadison

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