Nilpotent Orbits and Commutative Elements

✍ Scribed by C.Kenneth Fan; John R. Stembridge

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 212 KB
• Volume: 196
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1997.7119

✦ Synopsis

Let W be a simply laced Coxeter group with generating set S, and let W denote c the subset consisting of those elements whose reduced expressions have no substrings of the form sts for any non-commuting s, t g S. We give a root system characterization of W , and in the case where W corresponds to a finite Weyl c group, show that W is a union of Spaltenstein᎐Springer᎐Steinberg cells. The c latter is valid also for affine Weyl groups of type A, but not for type D or E.