Related papers: Normalizer decompositions of p-local compact group…

S.L. Woronowicz proved in 1991 that quantum SU(1,1) does not exist as a locally compact quantum group. Results by L.I. Korogodsky in 1994 and more recently by Woronowicz gave strong indications that the normalizer N of SU(1,1) in SL(2,C) is…

We study three restrictions on normalizers or centralizers in finite p-groups, namely: (i) |N_G(H) : H| <= p^k for every H non-normal in G, (ii) |N_G(<g>) : <g>| <= p^k for every <g> non-normal in G, and (iii) |C_G(g) : <g>| <= p^k for…

Let $G$ be a real linear algebraic group and $L$ a finitely generated cosimplicial group. We prove that the space of homomorphisms $Hom(L_n,G)$ has a homotopy stable decomposition for each $n\geq 1$. When $G$ is a compact Lie group, we show…

We consider the question whether a Sylow like theorem is valid in the normalized units of integral group rings of finite groups. After a short survey on the known results we show that this is the case for integral group rings of Frobenius…

We study the pro-$p$ group $G$ whose finite quotients give the prototypical Sylow $p$-subgroup of the general linear groups over a finite field of prime characteristic $p$. In this article, we extend the known results on the subgroup…

Self equivalences of classifying spaces of $p$-local compact groups are well understood by means of the algebraic structure that gives rise to them, but explicit descriptions are lacking. In this paper we use a construction of Robinson of…

The aim of this article is to present a simple generalized Plancherel formula for a locally compact unimodular topological group G of type I. This formula specializes to the Whittaker-Plancherel formula for a split reductive p-adic group of…

Let H be a subgroup of some locally compact group G. Assume H is approximable by discrete subgroups and G admits neighborhood bases which are "almost-invariant" under conjugation by finite subsets of H. Let $m: G \to \mathbb{C}$ be a…

We survey some recent advances in the homotopy theory of classifying spaces, and homotopical group theory. We focus on the classification of p-compact groups in terms of root data over the p-adic integers, and discuss some of its…

We use a classical result of McCord and reduction methods of finite spaces to prove a generalization of Thomason's theorem on homotopy colimits over posets. In particular this allows us to characterize the homotopy colimits of diagrams of…

Suppose that W is a finite, unitary, reflection group acting on the complex vector space V and X is a subspace of V. Define N to be the setwise stabilizer of X in W, Z to be the pointwise stabilizer, and C=N/Z. Then restriction defines a…

Kirillov's orbit theory provides a powerful tool for the investigation of irreducible unitary representations of many classes of Lie groups. In a previous paper we used a modification hereof, called monomial linearisation, to construct a…

We study properties and the structure of Cartan subgroups in a connected Lie group. We obtain a characterisation of Cartan subgroups which generalises W\"ustner's structure theorem for the same. We show that Cartan subgroups are same as…

Let $G$ be a residually finite, good group of finite virtual cohomological dimension. We prove that the natural monomorphism $G\hookrightarrow\hat{G}$ induces a bijective correspondence between conjugacy classes of finite $p$-subgroups of…

The main purpose of this paper is to introduce a method to stabilize certain spaces of homomorphisms from finitely generated free abelian groups to a Lie group $G$, namely $Hom(\mathbb Z^n,G)$. We show that this stabilized space of…

In this work, we give a description of the structure of the normal subgroups of a Sylow $p$-subgroup $W_n$ of $\mathrm{Sym}(p^n)$, showing that they contain a term from the lower central series with bounded index. To this end, we explicitly…

If G is a finite group and p is a prime number, we investigate the relationship between the p-modular decomposition numbers of characters of height zero in the principal p-block of G and the p-local structure of G.

In this paper, we develop a modified proof strategy for homological stability of linear groups, with the general linear groups serving as a primary example. Our arguments are more direct than those in the classical works of Quillen and…

In this memoir we extend the theory of global pseudo-differential operators to the setting of arbitrary sub-Riemannian structures on a compact Lie group. More precisely, given a compact Lie group $G$, and the sub-Laplacian $\mathcal{L}$…

We reformulate several basic notions of notions in finite group theory in terms of iterations of the lifting property (orthogonality) with respect to particular morphisms. Our examples include the notions being nilpotent, solvable, perfect,…