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Kawanaka Invariants for Representations of Weyl Groups

✍ Scribed by Akihiko Gyoja; Kyo Nishiyama; Kenji Taniguchi

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
219 KB
Volume
225
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

Let W be a Weyl group and let V be the natural ‫ރ‬W-module, i.e., the reflection representation. For a complex irreducible character of W, we consider the invariant

Ý wgW Ž . introduced by N. Kawanaka. We determine I ; q explicitly. Looking over these Ž . results, we observe a relation between Kawanaka's invariants I ; q and the two-sided cells. For example, if a two-sided cell consists of a single element , then Ž .

l Ž h i . Ž h i . the Kawanaka invariant I ; q can be expressed as Ł 1 q q r 1 y q with is 1 some integers h . This expression can be regarded as a quantization of the usual i hook formula for the dimension of irreducible representations of symmetric groups.

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