Journal of the Mathematical Society of Japan

Elementary divisors of Cartan matrices for symmetric groups

Katsuhiro UNO and Hiro-Fumi YAMADA

Full-text: Open access

Abstract

In this paper, we give an easy description of the elementary divisors of the Cartan matrices for symmetric groups in terms of the lengths of p -regular partitions and their Glaisher correspondents. Moreover, for p = 2 , it is done block wise. There we use certain kinds of cores and weights, which are similar to but different from the usual ones.

Article information

Source
J. Math. Soc. Japan, Volume 58, Number 4 (2006), 1031-1036.

Dates
First available in Project Euclid: 21 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1179759536

Digital Object Identifier
doi:10.2969/jmsj/1179759536

Mathematical Reviews number (MathSciNet)
MR2276180

Zentralblatt MATH identifier
1108.20009

Subjects
Primary: 20C20: Modular representations and characters
Secondary: 20C30: Representations of finite symmetric groups 05E10: Combinatorial aspects of representation theory [See also 20C30]

Keywords
Cartan matrix symmetric groups

Citation

UNO, Katsuhiro; YAMADA, Hiro-Fumi. Elementary divisors of Cartan matrices for symmetric groups. J. Math. Soc. Japan 58 (2006), no. 4, 1031--1036. doi:10.2969/jmsj/1179759536. https://projecteuclid.org/euclid.jmsj/1179759536


Export citation

References

  • C. Bessenrodt and J. B. Olsson, The 2-blocks of the covering groups of the symmetric groups, Adv. in Math., 129 (1997), 261–300.
  • C. Bessenrodt and J. B.Olsson, Spin representations and powers of 2, Algebr. Represent. Theory, 3 (2000), 289–300.
  • G. James and A. Kerber, The Representation Theory of the Symmetric Group, Encyclopedia of Math. Appl., 16, Addison-Wesley, 1981.
  • H. Nagao and Y. Tsushima, Representations of Finite Groups, Academic Press, Inc., Boston, 1989.
  • T. Nakajima and H.-F. Yamada, Schur's Q-functions and twisted affine Lie algebras, Combinatorial methods in representation theory (Kyoto, 1998), 241–259, Adv. Stud. Pure Math., 28, Kinokuniya, Tokyo, 2000.
  • J. B. Olsson, Lower defect groups in symmetric groups, J. Algebra, 104 (1986), 37–56.
  • J. B. Olsson, Combinatorics and representations of finite groups, Vorlesungen aus dem Fachbereich Mathematik der Universität GH Essen, 20, 1993.
  • M. Osima, Some remarks on the characters of the symmetric group, II, Canad. J. Math., 6 (1954), 511–521.