Bruhat order on the involutions of classical Weyl groups
2006 (English)In: Advances in Applied Mathematics, ISSN 0196-8858, E-ISSN 1090-2074, Vol. 37, no 1, 68-111 p.Article in journal (Refereed) Published
It is well known that a Coxeter group W, partially ordered by the Bruhat order, is a graded poset, with rank function given by the length, and that it is EL-shellable, hence Cohen-Macaulay, and Eulerian. We ask whether Invol(W), the subposet of W induced by the set of involutions, is endowed with similar properties. If W is of type A or B, we proved, respectively in [F. Incitti, The Bruhat order on the involutions of the symmetric group, J. Algebraic Combin. 20 (2004), 243-261] and [F. Incitti, The Bruhat order on the involutions of the hyperoctahedral group, European J. Combin. 24 (2003), 825-848], that Invol(W) is graded, EL-shellable and Eulerian. In this work we complete the investigation on the classical Weyl groups, extending these results to type D and providing a unified description for the rank function.
Place, publisher, year, edition, pages
2006. Vol. 37, no 1, 68-111 p.
coxeter groups, classical Weyl groups, Bruhat order, involutions, EL-shellability
IdentifiersURN: urn:nbn:se:kth:diva-37573DOI: 10.1016/j.aam.2005.11.002ISI: 000238050800005ScopusID: 2-s2.0-33646501952OAI: oai:DiVA.org:kth-37573DiVA: diva2:434326