Inversion arrangements and Bruhat intervals
2011 (English)In: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 118, no 7, 1897-1906 p.Article in journal (Refereed) Published
Let W be a finite Coxeter group. For a given w is an element of W, the following assertion may or may not be satisfied: (*) The principal Bruhat order ideal of w contains as many elements as there are regions in the inversion hyperplane arrangement of w. We present a type independent combinatorial criterion which characterises the elements w is an element of W that satisfy (*). A couple of immediate consequences are derived: (1) The criterion only involves the order ideal of w as an abstract poser. In this sense, (*) is a poset-theoretic property. (2) For W of type A, another characterisation of (*), in terms of pattern avoidance, was previously given in collaboration with Linusson, Shareshian and Sjostrand. We obtain a short and simple proof of that result. (3) If W is a Weyl group and the Schubert variety indexed by w is an element of W is rationally smooth, then w satisfies (*).
Place, publisher, year, edition, pages
Elsevier Science B.V., Amsterdam , 2011. Vol. 118, no 7, 1897-1906 p.
Bruhat interval; Bruhat graph; Inversion arrangement; Coxeter group
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-69764DOI: 10.1016/j.jcta.2011.04.005ISI: 000291900600001OAI: oai:DiVA.org:liu-69764DiVA: diva2:433632