Dual braid monoids, Mikado braids and positivity in Hecke algebras
| Autor: | François Digne, Thomas Gobet |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Monoid
Pure mathematics General Mathematics Braid group Group Theory (math.GR) Type (model theory) Characterization (mathematics) 01 natural sciences Mathematics - Geometric Topology Mathematics::Group Theory Mathematics::Category Theory Mathematics::Quantum Algebra 0103 physical sciences FOS: Mathematics Braid Mathematics - Combinatorics Representation Theory (math.RT) 0101 mathematics Mathematics::Representation Theory Mathematics Group (mathematics) 010102 general mathematics Geometric Topology (math.GT) Basis (universal algebra) Mathematics::Geometric Topology Combinatorics (math.CO) 010307 mathematical physics Mathematics - Group Theory Coxeter element Mathematics - Representation Theory |
| Zdroj: | Mathematische Zeitschrift. 285:215-238 |
| ISSN: | 1432-1823 0025-5874 |
| DOI: | 10.1007/s00209-016-1704-z |
| Popis: | We study the rational permutation braids, that is the elements of an Artin-Tits group of spherical type which can be written $x^{-1} y$ where $x$ and $y$ are prefixes of the Garside element of the braid monoid. We give a geometric characterization of these braids in type $A_n$ and $B_n$ and then show that in spherical types different from $D_n$ the simple elements of the dual braid monoid (for arbitrary choice of Coxeter element) embedded in the braid group are rational permutation braids (we conjecture this to hold also in type $D_n$).This property implies positivity properties of the polynomials arising in the linear expansion of their images in the Iwahori-Hecke algebra when expressed in the Kazhdan-Lusztig basis. In type $A_n$, it implies positivity properties of their images in the Temperley-Lieb algebra when expressed in the diagram basis. 26 pages, 8 figures |
| Databáze: | OpenAIRE |
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