RT Journal Article
T1 Parabolic subgroups acting on the additional length graph
A1 Antolín Pichel, Yago
A1 Cumplido, María
AB Let A ≠ A1;A2;I2m be an irreducible Artin–Tits group of spherical type. We show that the periodic elements of A and the elements preserving some parabolic subgroup of A act elliptically on the additional length graph CAL(A), a hyperbolic, infinite diameter graph associated to A constructed by Calvez and Wiest to show that A/Z(A) is acylindrically hyperbolic. We use these results to find an element g ∈ A such that <P,g> ≅ P * <g> for every proper standard parabolic subgroup P of A. The length of g is uniformly bounded with respect to the Garside generators, independently of A. This allows us to show that, in contrast with the Artin generators case, the sequence ω(An,S)(with n ∈ N) of exponential growth rates of braid groups, with respect to the Garside generating set, goes to infinity.
PB Mathematical Sciences Publishers (MSP)
SN 1472-2747
YR 2021
FD 2021
LK https://hdl.handle.net/20.500.14352/8624
UL https://hdl.handle.net/20.500.14352/8624
LA eng
NO Ministerio de Ciencia e Innovación (MICINN)
NO Ministerio de Economía y Competitividad (MINECO)
NO Junta de Andalucía
DS Docta Complutense
RD 13 may 2025