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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
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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
Email: christian.stump@fu-berlin.de

DOI: https://doi.org/10.1090/S0025-5718-2014-02841-X
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.