We give a version of Shimizu’s lemma for groups of complex hyperbolic isometries one of whose generators is a parabolic screw motion. Suppose that G is a discrete group containing a parabolic screw motion A and let B be any element of G not fixing the fixed point of A. Our result gives a bound on the radius of the isometric spheres of B and B−1 in terms of the translation lengths of A at their ...

This paper studies Emerton’s Jacquet module functor for locally analytic representations of p-adic reductive groups, introduced in [Eme06a]. When P is a parabolic subgroup whose Levi factor M is not commutative, we show that passing to an isotypical subspace for the derived subgroup ofM gives rise to essentially admissible locally analytic representations of the torus Z(M), which have a natural...

The aim of this note is to prove that the parabolic closure of any subset of a Coxeter group is a parabolic subgroup. To obtain that, several technical lemmas on the root system of a parabolic subgroup are established. MSC 2000 Subject Classifications: Primary 20F55; Secondary 20H15

The group AS is called an Artin group and relations sts . . . } {{ } ms,t terms = tst . . . } {{ } ms,t terms are called braid relations. For instance, if S = {s1, . . . , sn} with msi,sj = 3 for |i − j| = 1 and msi,sj = 2 otherwise, then the associated Artin group is the braid group. We denote by A+S the submonoid of AS generated by S. This monoid A+S has the same presentation as the group AS ...

Given a Chevalley group ${\mathbf G}(q)$ and parabolic subgroup $P\subset {\mathbf G}(q)$, we prove that for any set $A$ there is certain growth of relatively to $P$, namely, either $AP$ or $PA$ much larger than $A$. Also, study question about the intersection $A^n$ with subgroups $P$ large $n$. We apply our method obtain some results on modular form Zaremba’s conjecture from theory continued f...