26. CMB 2009 (vol 40 pp. 376)
27. CMB 2009 (vol 40 pp. 72)
28. CMB 2008 (vol 51 pp. 60)
 Janzen, David

F{\o}lner Nets for Semidirect Products of Amenable Groups
For unimodular semidirect products of locally compact amenable
groups $N$ and $H$, we show that one can always construct a
F{\o}lner net of the form $(A_\alpha \times B_\beta)$ for $G$, where
$(A_\alpha)$ is a strong form of F{\o}lner net for $N$ and
$(B_\beta)$ is any F{\o}lner net for $H$. Applications to the
Heisenberg and Euclidean motion groups are provided.
Categories:22D05, 43A07, 22D15, 43A20 

29. CMB 2007 (vol 50 pp. 632)
 Zelenyuk, Yevhen; Zelenyuk, Yuliya

Transformations and Colorings of Groups
Let $G$ be a compact topological group and let $f\colon G\to G$ be a
continuous transformation of $G$. Define $f^*\colon G\to G$ by
$f^*(x)=f(x^{1})x$ and let $\mu=\mu_G$ be Haar measure on $G$. Assume
that $H=\Imag f^*$ is a subgroup of $G$ and for every
measurable $C\subseteq H$,
$\mu_G((f^*)^{1}(C))=\mu_H(C)$. Then for every measurable
$C\subseteq G$, there exist $S\subseteq C$ and $g\in G$ such that
$f(Sg^{1})\subseteq Cg^{1}$ and $\mu(S)\ge(\mu(C))^2$.
Keywords:compact topological group, continuous transformation, endomorphism, Ramsey theoryinversion, Categories:05D10, 20D60, 22A10 

30. CMB 2007 (vol 50 pp. 460)
 Spielberg, Jack

Weak Semiprojectivity for Purely Infinite $C^*$Algebras
We prove that a separable, nuclear, purely infinite, simple
$C^*$algebra satisfying the universal coefficient theorem
is weakly semiprojective if and only if
its $K$groups are direct sums of cyclic groups.
Keywords:Kirchberg algebra, weak semiprojectivity, graph $C^*$algebra Categories:46L05, 46L80, 22A22 

31. CMB 2007 (vol 50 pp. 440)
 Raghuram, A.

A KÃ¼nneth Theorem for $p$Adic Groups
Let $G_1$ and $G_2$ be $p$adic groups. We describe a decomposition of
${\rm Ext}$groups in the category of smooth representations of
$G_1 \times G_2$ in terms of ${\rm Ext}$groups for $G_1$ and $G_2$.
We comment on ${\rm Ext}^1_G(\pi,\pi)$ for a supercuspidal
representation
$\pi$ of a $p$adic group $G$. We also consider an example of
identifying
the class, in a suitable ${\rm Ext}^1$, of a Jacquet module of certain
representations of $p$adic ${\rm GL}_{2n}$.
Categories:22E50, 18G15, 55U25 

32. CMB 2007 (vol 50 pp. 291)
33. CMB 2007 (vol 50 pp. 48)
 Dvorsky, Alexander

Tensor Square of the Minimal Representation of $O(p,q)$
In this paper, we study the tensor product $\pi=\sigma^{\min}\otimes
\sigma^{\min}$ of the minimal representation $\sigma^{\min}$ of $O(p,q)$ with
itself, and decompose $\pi$ into a direct integral of irreducible
representations. The decomposition is given in terms of the Plancherel measure
on a certain real hyperbolic space.
Category:22e46 

34. CMB 2006 (vol 49 pp. 578)
35. CMB 2005 (vol 48 pp. 505)
 Bouikhalene, Belaid

On the Generalized d'Alembert's and Wilson's Functional Equations on a Compact group
Let $G$ be a compact group. Let $\sigma$ be a continuous involution
of $G$. In this paper, we are
concerned by the following functional equation
$$\int_{G}f(xtyt^{1})\,dt+\int_{G}f(xt\sigma(y)t^{1})\,dt=2g(x)h(y), \quad
x, y \in G,$$ where $f, g, h \colonG \mapsto \mathbb{C}$, to be
determined, are complex continuous functions on $G$ such that $f$ is
central. This equation generalizes d'Alembert's and Wilson's
functional equations. We show that the solutions are expressed by
means of characters of irreducible, continuous and unitary
representations of the group $G$.
Keywords:Compact groups, Functional equations, Central functions, Lie, groups, Invariant differential operators. Categories:39B32, 39B42, 22D10, 22D12, 22D15 

36. CMB 2004 (vol 47 pp. 439)
 Parker, John R.

On the Stable Basin Theorem
The stable basin theorem was introduced by Basmajian and Miner as a
key step in their necessary condition for the discreteness of a
nonelementary group of complex hyperbolic isometries. In this
paper we improve several of Basmajian and Miner's key estimates and
so give a substantial improvement on the main inequality in the
stable basin theorem.
Categories:22E40, 20H10, 57S30 

37. CMB 2004 (vol 47 pp. 215)
 Jaworski, Wojciech

Countable Amenable Identity Excluding Groups
A discrete group $G$ is called \emph{identity excluding\/}
if the only irreducible
unitary representation of $G$ which weakly contains the $1$dimensional identity
representation is the $1$dimensional identity representation itself. Given a
unitary representation $\pi$ of $G$ and a probability measure $\mu$ on $G$, let
$P_\mu$ denote the $\mu$average $\int\pi(g) \mu(dg)$. The goal of this article
is twofold: (1)~to study the asymptotic behaviour of the powers $P_\mu^n$, and
(2)~to provide a characterization of countable amenable identity excluding groups.
We prove that for every adapted probability measure $\mu$ on an identity excluding
group and every unitary representation $\pi$ there exists and orthogonal projection
$E_\mu$ onto a $\pi$invariant subspace such that $s$$\lim_{n\to\infty}\bigl(P_\mu^n
\pi(a)^nE_\mu\bigr)=0$ for every $a\in\supp\mu$. This also remains true for suitably
defined identity excluding locally compact groups. We show that the class of countable
amenable identity excluding groups coincides with the class of $\FC$hypercentral
groups; in the finitely generated case this is precisely the class of groups of
polynomial growth. We also establish that every adapted random walk on a countable
amenable identity excluding group is ergodic.
Categories:22D10, 22D40, 43A05, 47A35, 60B15, 60J50 

38. CMB 2003 (vol 46 pp. 332)
 Đoković, Dragomir Z.; Tam, TinYau

Some Questions about Semisimple Lie Groups Originating in Matrix Theory
We generalize the wellknown result that a square traceless complex
matrix is unitarily similar to a matrix with zero diagonal to
arbitrary connected semisimple complex Lie groups $G$ and their Lie
algebras $\mathfrak{g}$ under the action of a maximal compact subgroup
$K$ of $G$. We also introduce a natural partial order on
$\mathfrak{g}$: $x\le y$ if $f(K\cdot x) \subseteq f(K\cdot y)$ for
all $f\in \mathfrak{g}^*$, the complex dual of $\mathfrak{g}$. This
partial order is $K$invariant and induces a partial order on the
orbit space $\mathfrak{g}/K$. We prove that, under some restrictions
on $\mathfrak{g}$, the set $f(K\cdot x)$ is starshaped with respect
to the origin.
Categories:15A45, 20G20, 22E60 

39. CMB 2002 (vol 45 pp. 466)
 Arthur, James

A Note on the Automorphic Langlands Group
Langlands has conjectured the existence of a universal group, an
extension of the absolute Galois group, which would play a fundamental
role in the classification of automorphic representations. We shall
describe a possible candidate for this group. We shall also describe
a possible candidate for the complexification of Grothendieck's
motivic Galois group.
Categories:11R39, 22E55 

40. CMB 2002 (vol 45 pp. 436)
41. CMB 2002 (vol 45 pp. 364)
 Deitmar, Anton

Mellin Transforms of Whittaker Functions
In this note we show that for an arbitrary reductive Lie group
and any admissible irreducible Banach representation the Mellin
transforms of Whittaker functions extend to meromorphic functions.
We locate the possible poles and show that they always lie along
translates of walls of Weyl chambers.
Categories:11F30, 22E30, 11F70, 22E45 

42. CMB 2002 (vol 45 pp. 220)
 Hakim, Jeffrey; Murnaghan, Fiona

Globalization of Distinguished Supercuspidal Representations of $\GL(n)$
An irreducible supercuspidal representation $\pi$ of $G=
\GL(n,F)$, where $F$ is a nonarchimedean local field of
characteristic zero, is said to be ``distinguished'' by a
subgroup $H$ of $G$ and a quasicharacter $\chi$ of $H$ if
$\Hom_H(\pi,\chi)\noteq 0$. There is a suitable global analogue
of this notion for and irreducible, automorphic, cuspidal
representation associated to $\GL(n)$. Under certain general
hypotheses, it is shown in this paper that every distinguished,
irreducible, supercuspidal representation may be realized as a
local component of a distinguished, irreducible automorphic,
cuspidal representation. Applications to the theory of
distinguished supercuspidal representations are provided.
Categories:22E50, 22E35, 11F70 

43. CMB 2001 (vol 44 pp. 491)
 Wang, Weiqiang

Resolution of Singularities of Null Cones
We give canonical resolutions of singularities of several cone
varieties arising from invariant theory. We establish a connection
between our resolutions and resolutions of singularities of closure of
conjugacy classes in classical Lie algebras.
Categories:14L35, 22G 

44. CMB 2001 (vol 44 pp. 482)
45. CMB 2001 (vol 44 pp. 429)
 Henniger, J. P.

Ergodic Rotations of Nilmanifolds Conjugate to Their Inverses
In answer to a question posed in \cite{G}, we give sufficient
conditions on a Lie nilmanifold so that any ergodic rotation of the
nilmanifold is metrically conjugate to its inverse. The condition is
that the Lie algebra be what we call quasigraded, and is weaker than
the property of being graded. Furthermore, the conjugating map can be
chosen to be an involution. It is shown that for a special class of
groups, the condition of quasigraded is also necessary. In certain
examples there is a continuum of conjugacies.
Categories:28Dxx, 22E25 

46. CMB 2001 (vol 44 pp. 408)
47. CMB 2001 (vol 44 pp. 298)
48. CMB 2000 (vol 43 pp. 459)
 Ndogmo, J. C.

Properties of the Invariants of Solvable Lie Algebras
We generalize to a field of characteristic zero certain properties of
the invariant functions of the coadjoint representation of solvable
Lie algebras with abelian nilradicals, previously obtained over the
base field $\bbC$ of complex numbers. In particular we determine
their number and the restricted type of variables on which they
depend. We also determine an upper bound on the maximal number of
functionally independent invariants for certain families of solvable
Lie algebras with arbitrary nilradicals.
Categories:17B30, 22E70 

49. CMB 2000 (vol 43 pp. 380)
50. CMB 2000 (vol 43 pp. 90)