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Springer theory in braid groups and the Birman-Ko-Lee monoid. (English) Zbl 1056.20023
Summary: We state a conjecture about centralizers of certain roots of central elements in braid groups, and check it for braid groups of type \(A\), \(B\), \(G(d,1,r)\) and a couple of other cases. Our proof makes use of results of J. Birman, K. H. Ko, and S. J. Lee [Adv. Math. 139, No. 2, 322-353 (1998; Zbl 0937.20016)], of which we give a new intrinsic account.

MSC:
20F36 Braid groups; Artin groups
20F55 Reflection and Coxeter groups (group-theoretic aspects)
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