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In this talk, I will breifly introduce the p-aidc number, p-aidc manifolds, p-adic algebraic groups and p-aidc definable groups. Using an elementary method, I will show that every open subgroup of a c...
(For convenience we shall henceforth assume that n is torsionfree: by Selberg's lemma [12] this may be accomplished by replacing TT by a subgroup of finite index. This insures that M is a compact ...
Let G denote a connected reductive group, de ned and split over Z, and let M  G denote a Levi subgroup. In this paper we study varieties of geodesic triangles with xed vector-valued side-lengths ...
ON PARAHORIC SUBGROUPS     PARAHORIC SUBGROUPS  trajectory       2015/9/29
We give the proofs of some simple facts on parahoric subgroups and on Iwahori Weyl groups used in [H], [PR] and in [R].
An abeloid space over a rigid space S over a non-archimedean field k is a proper smooth S-group A → S with connected fibers. Relative ampleness (in the sense of [C3]) gives a good notion ...
Let $R$ be a subset of a group $G$. We call a subgroup $H$ of $G$ the $R$-conjugate-permutable subgroup of $G$, if $HH^{x}=H^{x}H$ for all $x\in R$. This concept is a generalization of conjugate-permu...
A normal Hall subgroup N of a group G is a normal subgroup with its order coprime with its index. Schur-Zassenhaus theorem states that every normal Hall subgroup has a complement subgroup, that is a s...
Adequate subgroups     adequate subgroups  Number Theory       2011/9/23
Abstract: We study adequate subgroups of $GL_n$ over a finite field. This notion is useful in the study of automorphy lifting theorems. In particular, we give a sufficient condition for a subgroup to ...
Abstract: For an arbitrary connected solvable spherical subgroup H of a connected semisimple algebraic group G we compute the group N_G(H), the normalizer of H in G. Thereby we complete a classificati...
Abstract: Let (G, *) be a semigroup, D subset of G, and n >= 2 be an integer. We say that (D, *) is an n-closed subset of G if a_1* ... *a_n in D for every a_1, ..., a_n in D. Hence every closed set i...
Abstract: We describe some of the geometric properties of the automorphism group Aut(F) of Thompson's group F. We give realizations of Aut(F) geometrically via periodic tree pair diagrams, which lead ...
Abstract: Let $G$ be a non-elementary hyperbolic group. Let $w$ be a group word such that the set $w[G]$ of all its values in $G$ does not coincide with $G$ or 1. We show that the width of verbal subg...
Abstract: In this paper, we study the restriction of Zuckerman's derived functor (g,K)-modules A_q(\lambda) to g' for symmetric pairs of reductive Lie algebras (g,g'). When the restriction decomposes ...
For simply connected compact exceptional Lie groups G = F4,E6 and E7, we consider two involutions σ, γ and determine the group structure of subgroups G,of G which are the intersection G ∩ G of the ...

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