## Journal of the Mathematical Society of Japan

### Elementary divisors of Cartan matrices for symmetric groups

#### 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

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

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