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1. CMB 2011 (vol 54 pp. 663)
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 Richardson-Springer Poset. In particular, for $\Phi$ irreducible,
the ascending Richardson-Springer Poset of $\mathcal{I}_{\theta}$,
for nontrivial $\theta$ is identical to the descending
Richardson-Springer Poset of $\mathcal{I}_{\operatorname{Id}}$.
Categories:20G15, 20G20, 22E15, 22E46, 43A85 |
2. CMB 2000 (vol 43 pp. 47)
A Property of Lie Group Orbits Let $G$ be a real Lie group and $X$ a real analytic manifold.
Suppose that $G$ acts analytically on $X$ with finitely many
orbits. Then the orbits are subanalytic in $X$. As a consequence
we show that the micro-support of a $G$-equivariant sheaf on $X$ is
contained in the conormal variety of the $G$-action.
Categories:32B20, 22E15 |
3. CMB 1998 (vol 41 pp. 368)
Exponentiality of certain real solvable Lie groups In this article, making use of the second author's criterion for
exponentiality of a connected solvable Lie group, we give a rather
simple necessary and sufficient condition for the semidirect
product of a torus acting on certain connected solvable Lie groups
to be exponential.
Categories:22E25, 22E15 |