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Article Dans Une Revue Israel Journal of Mathematics Année : 2021

Transverse properties of parabolic subgroups of Garside groups

Résumé

Let G be a Garside group endowed with the generating set S of non-trivial simple elements, and let H be a parabolic subgroup of G. We determine a transversal T of H in G such that each theta is an element of T is of minimal length in its right-coset, H theta, for the word length with respect to S. We show that there exists a regular language L on S boolean OR S-1 and a bijection ev: L -> T satisfying lg(U) = lg(S)(ev(U)) for all U is an element of L. From this we deduce that the coset growth series of H in G is rational. Finally, we show that G has fellow projections on H but does not have bounded projections on H.

Dates et versions

hal-03303508 , version 1 (28-07-2021)

Identifiants

Citer

Yago Antolín, Luis Paris. Transverse properties of parabolic subgroups of Garside groups. Israel Journal of Mathematics, 2021, 241 (2), pp.501-526. ⟨10.1007/s11856-021-2100-x⟩. ⟨hal-03303508⟩
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