## Journal of the Mathematical Society of Japan

### Invariants for representations of Weyl groups and two-sided cells

#### Abstract

The notion of two-sided cell, which was originally introduced by A. Joseph and reformulated by D. Kazhdan and G. Lusztig, has played an important role in the representation theory. Results concerning them have been obtained by very deep and sometimes ad hoc arguments. Here we introduce certain polynomial invariants for irreducible representations of Weyl groups. Our invariants are easily calculated, and the calculational results show that they almost determine the two-sided cells. Moreover, the factorization pattern of our polynomial invariants seems to be controlled by the natural parameter set $\mathscr{M}(\mathscr{G})$ of each two-sided cell.

#### Article information

Source
J. Math. Soc. Japan, Volume 51, Number 1 (1999), 1-34.

Dates
First available in Project Euclid: 10 June 2008

https://projecteuclid.org/euclid.jmsj/1213108348

Digital Object Identifier
doi:10.2969/jmsj/05110001

Mathematical Reviews number (MathSciNet)
MR1661012

Zentralblatt MATH identifier
0928.20035

#### Citation

GYOJA, Akihiko; NISHIYAMA, Kyo; SHIMURA, Hiroyuki. Invariants for representations of Weyl groups and two-sided cells. J. Math. Soc. Japan 51 (1999), no. 1, 1--34. doi:10.2969/jmsj/05110001. https://projecteuclid.org/euclid.jmsj/1213108348