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Transactions of the American Mathematical Society

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Computing reflection length in an affine Coxeter group


Authors: Joel Brewster Lewis, Jon McCammond, T. Kyle Petersen and Petra Schwer
Journal: Trans. Amer. Math. Soc. 371 (2019), 4097-4127
MSC (2010): Primary 20F55
DOI: https://doi.org/10.1090/tran/7472
Published electronically: December 7, 2018
MathSciNet review: 3917218
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Abstract: In any Coxeter group, the conjugates of elements in its Coxeter generating set are called reflections, and the reflection length of an element is its length with respect to this expanded generating set. In this article we give a simple formula that computes the reflection length of any element in any affine Coxeter group and we provide a simple uniform proof.


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Additional Information

Joel Brewster Lewis
Affiliation: Department of Mathematics, George Washington University, Washington, DC 20052
Email: jblewis@gwu.edu

Jon McCammond
Affiliation: Department of Mathematics, University of California, Santa Barbara, Santa Barbara, California 93106
Email: jon.mccammond@math.ucsb.edu

T. Kyle Petersen
Affiliation: Department of Mathematical Sciences, De Paul University, Chicago, Illinois 60614
Email: tpeter21@depaul.edu

Petra Schwer
Affiliation: Department of Mathematics, Karlsruhe Institute of Technology, Englerstrasse 2, 76133 Karlsruhe, Germany
Email: petra.schwer@kit.edu

DOI: https://doi.org/10.1090/tran/7472
Received by editor(s): October 18, 2017
Received by editor(s) in revised form: November 21, 2017
Published electronically: December 7, 2018
Additional Notes: The first author’s work was supported by NSF grant DMS-1401792
The third author’s work was supported by a Simons Foundation collaboration travel grant.
The fourth author’s work was supported by DFG grant SCHW 1550 4-1 within SPP 2026.
Article copyright: © Copyright 2018 American Mathematical Society