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Twisted identities in Coxeter groups
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2008 (English)In: Journal of Algebraic Combinatorics, ISSN 0925-9899, E-ISSN 1572-9192, Vol. 28, no 2, 313-332 p.Article in journal (Refereed) Published
Abstract [en]

Given a Coxeter system ( W, S) equipped with an involutive automorphism theta, the set of twisted identities is iota(theta) = {theta(w(-1))w vertical bar w is an element of W}. We point out how iota(theta) shows up in several contexts and prove that if there is no s is an element of S such that s theta(s) is of odd order greater than 1, then the Bruhat order on iota(theta) is a graded poset with rank function. given by halving the Coxeter length. Under the same condition, it is shown that the order complexes of the open intervals either are PL spheres or Z-acyclic. In the general case, contractibility is shown for certain classes of intervals. Furthermore, we demonstrate that sometimes these posets are not graded. For the Poincare series of iota(theta), i.e. its generating function with respect to rho, a factorisation phenomenon is discussed.

Place, publisher, year, edition, pages
2008. Vol. 28, no 2, 313-332 p.
Keyword [en]
Coxeter groups, Bruhat order, twisted identities, twisted involutions, bruhat order, symmetrical varieties, involutions
URN: urn:nbn:se:kth:diva-17744DOI: 10.1007/s10801-007-0106-zISI: 000258154200005ScopusID: 2-s2.0-49149125447OAI: diva2:335789
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

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Hultman, Axel
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