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On the minimal positive standardizer of a parabolic subgroup of an Artin–Tits group

Authors
  • Cumplido, María1, 2
  • 1 Univ Rennes, CNRS, IRMAR - UMR 6625, Rennes, 35000, France , Rennes (France)
  • 2 Universidad de Sevilla, Depto. de Álgebra, Instituto de Matemáticas (IMUS), Av. Reina Mercedes s/n, Seville, 41012, Spain , Seville (Spain)
Type
Published Article
Journal
Journal of Algebraic Combinatorics
Publisher
Springer US
Publication Date
Sep 22, 2018
Volume
49
Issue
3
Pages
337–359
Identifiers
DOI: 10.1007/s10801-018-0837-z
Source
Springer Nature
Keywords
License
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Abstract

The minimal standardizer of a curve system on a punctured disk is the minimal positive braid that transforms it into a system formed only by round curves. We give an algorithm to compute it in a geometrical way. Then, we generalize this problem algebraically to parabolic subgroups of Artin–Tits groups of spherical type and we show that, to compute the minimal standardizer of a parabolic subgroup, it suffices to compute the pn-normal form of a particular central element.

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