Journal of the Mathematical Society of Japan

Invariants for representations of Weyl groups and two-sided cells

Akihiko GYOJA, Kyo NISHIYAMA, and Hiroyuki SHIMURA

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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 M(G) of each two-sided cell.

Article information

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

First available in Project Euclid: 10 June 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20H15: Other geometric groups, including crystallographic groups [See also 51-XX, especially 51F15, and 82D25]
Secondary: 20G05: Representation theory 05A03

representations of Weyl groups two-sided cells


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.

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