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Let $mathsf G$ be a connected reductive linear algebraic group defined over $mathbb R$, and let $C: mathsf Grightarrow mathsf G$ be a fundamental Chevalley involution. We show that for every $gin mathsf G(mathbb R)$, $C(g)$ is conjugate to $g^{-1}$ in the group $mathsf G(mathbb R)$. Similar result on the Lie algebras is also obtained.
We define a map from the set of conjugacy classes of a Weyl group W to the representation ring of W tensored with the ring of polynomials in one variable.
Let $G$ be a connected complex semisimple Lie group with a fixed maximal torus $T$ and a Borel subgroup $B supset T$. For an arbitrary automorphism $theta$ of $G$, we introduce a holomorphic Poisson structure $pi_theta$ on $G$ which is invariant unde
The twin group $T_n$ is a right angled Coxeter group generated by $n-1$ involutions and the pure twin group $PT_n$ is the kernel of the natural surjection from $T_n$ onto the symmetric group on $n$ symbols. In this paper, we investigate some structur
We show that if a f.g. group $G$ has a non-elementary WPD action on a hyperbolic metric space $X$, then the number of $G$-conjugacy classes of $X$-loxodromic elements of $G$ coming from a ball of radius $R$ in the Cayley graph of $G$ grows exponentia
We investigate the natural codings of linear involutions. We deduce from the geometric representation of linear involutions as Poincare maps of measured foliations a suitable definition of return words which yields that the set of first return words