Experimental Mathematics

Calculating Canonical Distinguished Involutions in the Affine Weyl Groups

Tanya Chmutova and Viktor Ostrik

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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. We calculate the canonical distinguished involutions in the affine Weyl groups of rank ≤ 7. We also prove some partial results relating canonical distinguished involutions and Dynkin's diagrams of the nilpotent orbits in the Langlands dual group.

Article information

Experiment. Math., Volume 11, Issue 1 (2002), 99-117.

First available in Project Euclid: 10 July 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 17B20: Simple, semisimple, reductive (super)algebras
Secondary: 20H15: Other geometric groups, including crystallographic groups [See also 51-XX, especially 51F15, and 82D25]

affine Weyl groups cells nilpotent orbits in semisimple Lie algebras


Chmutova, Tanya; Ostrik, Viktor. Calculating Canonical Distinguished Involutions in the Affine Weyl Groups. Experiment. Math. 11 (2002), no. 1, 99--117. https://projecteuclid.org/euclid.em/1057860319

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