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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
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).
S. Ariki, “On the semisimplicity of the Hecke algbera of (ℤ/rℤ)≀S n ,” J. Algebra, 169, 216–225 (1994).
I. Cherednik, “A new interpretation of Gelfand-Tzetlin bases,” Duke Math. J., 54, 563–577 (1987).
C. Curtis and I. Reiner, Methods of Representation Theory: With Applications to Finite Groups and Orders, Vol. II, Wiley, New York (1987).
A. Gyoja and K. Uno, “On the semisimplicity of Hecke algebras,” J. Math. Soc. Japan, 41, 75–79 (1989).
T. Halverson, “Representations of the q-rook monoid,” preprint (2001).
P. N. Hoefsmit, “Representations of Hecke algebras of finite groups with BN-pairs of classical type,” Thesis, Univ. of British Columbia (1974).
I. G. Macdonald, Symmetric Functions and Hall Polynomials, 2 ed., Oxford University Press, New York (1995).
P. P. Martin and D. Woodcock, “On the structure of the blob algebra,” J. Algebra, 225, 957–988 (2000).
W. D. Munn, “Matrix representations of semigroups,” Proc. Camb. Phil. Soc., 53, 5–12 (1957).
W. D. Munn, “The characters of the symmetric inverse semigroup,” Proc. Camb. Phil. Soc., 53, 13–18 (1957).
R. Orellana and A. Ram, “Affine braids, Markov traces and the category O,” Preprint (2001).
A. Ram, “Skew shape representations are irreducible,” preprint (1998).
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).
L. Solomon, “Representations of the rook monoid,” J. Algebra (to appear).
L. Solomon, “Abstract No. 900-16-169,” in: Abstracts Presented to the American Math. Soc., Vol. 16,No. 2, Spring (1995).
L. Solomon, “The Iwahori algebra of M n(F q), a presentation and a representation on tensor space,” Preprint (2001).
S. Sakamoto and T. Shoji, “Schur-Weyl reciprocity for Ariki-Koike algebras,” J. Algebra, 221, 293–314 (1999).
A. Young, “On quantitative substitutional analysis. VI,” Proc. London Math. Soc., 31, 253–289 (1931).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Halverson, T., Ram, A. q-Rook Monoid Algebras, Hecke Algebras, and Schur–Weyl Duality. Journal of Mathematical Sciences 121, 2419–2436 (2004). https://doi.org/10.1023/B:JOTH.0000024623.99412.13
Issue Date:
DOI: https://doi.org/10.1023/B:JOTH.0000024623.99412.13