On root posets for noncrystallographic root systems
Authors:
Michael Cuntz and Christian Stump
Journal:
Math. Comp. 84 (2015), 485-503
MSC (2010):
Primary 20F55
DOI:
https://doi.org/10.1090/S0025-5718-2014-02841-X
Published electronically:
May 28, 2014
MathSciNet review:
3266972
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We discuss properties of root posets for finite crystallographic root systems, and show that these properties uniquely determine root posets for the noncrystallographic dihedral types and type $H_3$, while proving that there does not exist a poset satisfying all of the properties in type $H_4$. We do this by exhaustive computer searches for posets having these properties. We further give a realization of the poset of type $H_3$ as restricted roots of type $D_6$, and conjecture a Hilbert polynomial for the $q,t$-Catalan numbers for type $H_4$.
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Additional Information
Michael Cuntz
Affiliation:
Fachbereich Mathematik, Universität Kaiserslautern, Germany
Address at time of publication:
Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Fakultät für Mathematik und Physik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
Email:
cuntz@math.uni-hannover.de
Christian Stump
Affiliation:
Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Fakultät für Mathematik und Physik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
Address at time of publication:
Institut für Mathematik, Freie Universität Berlin, Germany
MR Author ID:
904921
ORCID:
0000-0002-9271-8436
Email:
christian.stump@fu-berlin.de
Received by editor(s):
December 5, 2012
Received by editor(s) in revised form:
April 11, 2013, and May 10, 2013
Published electronically:
May 28, 2014
Additional Notes:
Most of the results of this article were achieved at the Leibniz Universität Hannover in summer 2012.
Article copyright:
© Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
