Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 51, Number 1 (1999), 1-34.
Invariants for representations of Weyl groups and two-sided cells
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 of each two-sided cell.
J. Math. Soc. Japan, Volume 51, Number 1 (1999), 1-34.
First available in Project Euclid: 10 June 2008
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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