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2002 Calculating Canonical Distinguished Involutions in the Affine Weyl Groups
Tanya Chmutova, Viktor Ostrik
Experiment. Math. 11(1): 99-117 (2002).


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.


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Tanya Chmutova. Viktor Ostrik. "Calculating Canonical Distinguished Involutions in the Affine Weyl Groups." Experiment. Math. 11 (1) 99 - 117, 2002.


Published: 2002
First available in Project Euclid: 10 July 2003

zbMATH: 1027.17006
MathSciNet: MR1960305

Primary: 17B20
Secondary: 20H15

Keywords: affine Weyl groups , cells , nilpotent orbits in semisimple Lie algebras

Rights: Copyright © 2002 A K Peters, Ltd.


Vol.11 • No. 1 • 2002
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