Related papers: On Chevalley restriction theorem

Let $\sigma_1$ and $\sigma_2$ be commuting involutions of a semisimple algebraic group $G$. This yields a $Z_2\times Z_2$-grading of $\g=\Lie(G)$, $\g=\bigoplus_{i,j=0,1}\g_{ij}$, and we study invariant-theoretic aspects of this…

For a cyclic group $A$ and a connected Lie group $G$ with an $A$-module structure (with the additional conditions that $G$ is compact and the $A$-module structure on $G$ is 1-semisimple if $A\cong\ZZ$), we define the twisted Weyl group…

For a finite p-group G and a bounded below G-spectrum X of finite type mod p, the G-equivariant Segal conjecture for X asserts that the canonical map X^G --> X^{hG} is a p-adic equivalence. Let C_{p^n} be the cyclic group of order p^n. We…

We study C*-algebras associated to right LCM semigroups, that is, semigroups which are left cancellative and for which any two principal right ideals are either disjoint or intersect in another principal right ideal. If $P$ is such a…

We prove that bi-invariant word metrics are bounded on certain Chevalley groups. As an application we provide restrictions on Hamiltonian actions of such groups.

Building upon work of Y. Shalom we give a homological-algebra flavored definition of an induction map in group homology associated to a topological coupling. As an application we obtain estimates of the (co)homological dimension of groups G…

An isovariant map is an equivariant map between $G$-spaces which strictly preserves isotropy groups. We consider an isovariant analogue of Klein--Williams equivariant intersection theory for a finite group $G$. We prove that under certain…

Suppose that a finite group $G$ admits an automorphism $\varphi $ of order $2^n$ such that the fixed-point subgroup $C_G(\varphi ^{2^{n-1}})$ of the involution $\varphi ^{2^{n-1}}$ is nilpotent of class $c$. Let $m=|C_G(\varphi)|$ be the…

We consider the natural Lie algebra structure on the (associative) group algebra of a finite group $G$, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a…

In this article we describe the $G\times G$-equivariant $K$-ring of $X$, where $X$ is a regular compactification of a connected complex reductive algebraic group $G$. Furthermore, in the case when $G$ is a semisimple group of adjoint type,…

Let G be a Chevalley group scheme of rank l. We show that the following holds for some absolute constant d>0 and two functions p_0=p_0(l) and C=C(l,p). Let p>p_0 be a prime number and let G_n:=G(\Z/p^n\Z) be the family of finite groups for…

Let $W\subset GL(V)$ be a complex reflection group, and ${\mathscr A}(W)$ the set of the mirrors of the complex reflections in $W$. It is known that the complement $X({\mathscr A}(W))$ of the reflection arrangement ${\mathscr A}(W)$ is a…

Let $\A$ be an algebra and $\sigma$ an automorphism of $\A$. A linear map $d$ of $\A$ is called a $\sigma$-derivation of $\A$ if $d(xy) = d(x)y + \sigma(x)d(y)$, for all $x, y \in \A$. A bilinear map $D: \A \times \A \to \A$ is said to be a…

In this paper we prove that every automorphism of a Chevalley group with the root system G_2 over a commutative ring R with 1/3, generated by all its invertible elements and the ideal 2R is a composition of ring and inner automorphisms.

We prove a finite-dimensional covariant Stinespring theorem for compact quantum groups. Let G be a compact quantum group, and let T:= Rep(G) be the rigid C*-tensor category of finite-dimensional continuous unitary representations of G. Let…

The coadjoint representation of a connected algebraic group $Q$ with Lie algebra $\mathfrak q$ is a thrilling and fascinating object. Symmetric invariants of $\mathfrak q$ (= $\mathfrak q$-invariants in the symmetric algebra $S(\mathfrak…

Let G be a simple, simply connected algebraic group defined over an algebraically closed field k of positive characteristic p. Let \sigma:G->G be a strict endomorphism (i. e., the subgroup G(\sigma) of \sigma-fixed points is finite). Also,…

Let $A$ be an abelian group and let $\iota$ be the automorphism of $A$ defined by $i:a\mapsto a^{-1}$. A Cayley graph $\Gamma=\mathrm{Cay}(A,S)$ is said to have an automorphism group \emph{as small as possible} if $\mathrm{Aut}(\Gamma)=…

Given a reflection group $G$ acting on a complex vector space $V$, a reflection map is the composition of an embedding $X \hookrightarrow V$ with the orbit map $V\to\mathbb C^p$ that maps a $G$-orbit to a point. Reflection maps can be very…

Let $G$ be a connected semisimple algebraic group with Lie algebra $g$ and $P$ a parabolic subgroup of $G$ with $Lie(P)=p$. The parabolic contraction of $g$ is the semi-direct product of $p$ and a $p$-module $g/p$ regarded as an abelian…