1. CMB 2017 (vol 61 pp. 174)
 Roche, Alan; Vinroot, C. Ryan

A factorization result for classical and similitude groups
For most classical and similitude groups, we show that each element
can be written as a product of two transformations that
a) preserve or almost preserve the underlying form and b) whose
squares are certain scalar maps. This generalizes work of Wonenburger
and Vinroot.
As an application, we reprove and slightly extend a well known
result of MÅglin, VignÃ©ras and Waldspurger on the existence
of automorphisms of $p$adic classical groups that take each
irreducible smooth representation to its dual.
Keywords:classical group, similitude group, involution, $p$adic group, dual of representation Categories:20G15, 22E50 

2. CMB 2016 (vol 59 pp. 824)
 Karpenko, Nikita A.

Incompressibility of Products of Pseudohomogeneous Varieties
We show that the conjectural criterion of $p$incompressibility
for products of projective homogeneous varieties in terms of
the factors, previously known in a few special cases only, holds
in general.
Actually, the proof goes through for a wider class of varieties
which includes the norm varieties associated to symbols in Galois
cohomology of arbitrary degree.
Keywords:algebraic groups, projective homogeneous varieties, Chow groups and motives, canonical dimension and incompressibility Categories:20G15, 14C25 

3. CMB 2013 (vol 56 pp. 795)
 MacDonald, Mark L.

Upper Bounds for the Essential Dimension of $E_7$
This paper gives a new upper bound for the essential dimension and the
essential 2dimension of the split simply connected group of type
$E_7$ over a field of characteristic not 2 or 3. In particular,
$\operatorname{ed}(E_7) \leq 29$, and $\operatorname{ed}(E_7;2) \leq 27$.
Keywords:$E_7$, essential dimension, stabilizer in general position Categories:20G15, 20G41 

4. CMB 2012 (vol 57 pp. 97)
 Levy, Jason

Rationality and the JordanGattiViniberghi decomposition
We verify
our earlier conjecture
and use it to prove that the
semisimple parts of the rational JordanKacVinberg decompositions of
a rational vector all lie in a single rational orbit.
Keywords:reductive group, $G$module, Jordan decomposition, orbit closure, rationality Categories:20G15, 14L24 

5. CMB 2011 (vol 54 pp. 663)
 Haas, Ruth; G. Helminck, Aloysius

Admissible Sequences for Twisted Involutions in Weyl Groups
Let $W$ be a Weyl group, $\Sigma$ a set of simple reflections in $W$
related to a basis $\Delta$ for the root system $\Phi$ associated with
$W$ and $\theta$ an involution such that $\theta(\Delta) = \Delta$. We
show that the set of $\theta$twisted involutions in $W$,
$\mathcal{I}_{\theta} = \{w\in W \mid \theta(w) = w^{1}\}$ is in one
to one correspondence with the set of regular involutions
$\mathcal{I}_{\operatorname{Id}}$. The elements of $\mathcal{I}_{\theta}$ are
characterized by sequences in $\Sigma$ which induce an ordering called
the RichardsonSpringer Poset. In particular, for $\Phi$ irreducible,
the ascending RichardsonSpringer Poset of $\mathcal{I}_{\theta}$,
for nontrivial $\theta$ is identical to the descending
RichardsonSpringer Poset of $\mathcal{I}_{\operatorname{Id}}$.
Categories:20G15, 20G20, 22E15, 22E46, 43A85 

6. CMB 2008 (vol 51 pp. 114)
 Petrov, V.; Semenov, N.; Zainoulline, K.

Zero Cycles on a Twisted Cayley Plane
Let $k$ be a field of characteristic not $2,3$.
Let $G$ be an exceptional simple algebraic group over $k$
of type $\F$, $^1{\E_6}$ or $\E_7$ with trivial Tits algebras.
Let $X$ be a projective $G$homogeneous variety.
If $G$ is of type $\E_7$, we assume in addition
that the respective
parabolic subgroup is of type $P_7$.
The main result of the paper says that
the degree map on the group of zero cycles of $X$
is injective.
Categories:20G15, 14C15 

7. CMB 2006 (vol 49 pp. 196)
8. CMB 2003 (vol 46 pp. 204)
 Levy, Jason

Rationality and Orbit Closures
Suppose we are given a finitedimensional vector space $V$ equipped
with an $F$rational action of a linearly algebraic group $G$, with
$F$ a characteristic zero field. We conjecture the following: to each
vector $v\in V(F)$ there corresponds a canonical $G(F)$orbit of
semisimple vectors of $V$. In the case of the adjoint action, this
orbit is the $G(F)$orbit of the semisimple part of $v$, so this
conjecture can be considered a generalization of the Jordan
decomposition. We prove some cases of the conjecture.
Categories:14L24, 20G15 

9. CMB 2002 (vol 45 pp. 388)
 Gille, Philippe

AlgÃ¨bres simples centrales de degrÃ© 5 et $E_8$
As a consequence of a theorem of RostSpringer, we establish that the
cyclicity problem for central simple algebra of degree~5 on fields
containg a fifth root of unity is equivalent to the study of
anisotropic elements of order 5 in the split group of type~$E_8$.
Keywords:algÃ¨bres simples centrales, cohomologie galoisienne Categories:16S35, 12G05, 20G15 
