Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
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
Identifiers
URN: urn:nbn:se:kth:diva-17744DOI: 10.1007/s10801-007-0106-zISI: 000258154200005Scopus ID: 2-s2.0-49149125447OAI: oai:DiVA.org:kth-17744DiVA: diva2:335789
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Hultman, Axel
By organisation
Mathematics (Div.)
In the same journal
Journal of Algebraic Combinatorics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 28 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf