Calculating canonical distinguished involutions in the affine Weyl groups

Details Calculating canonical distinguished involutions in the affine Weyl groups Calculating canonical distinguished involutions in the affine Weyl groups

2001-06-02

arxiv.org/abs/math/0106011v1

Mathematics

Representation Theory

21 pages

Scientific paper

Distinguished involutions in the affine Weyl groups, defined by G. Lusztig, play an essential role in the Kazhdan-Lusztig combinatorics of these groups. A distinguished involution is called canonical if it is the shortest element in its double coset with respect to the finite Weyl group. Each two-sided cell in the affine Weyl group contains precisely one canonical distinguished involution. In this note we calculate the canonical distinguished involutions in the affine Weyl groups of rank <8. We also prove some partial results relating canonical distinguished involutions and Dynkin's diagrams of the nilpotent orbits in the Langlands dual group.

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