Related papers: On relative complete reducibility

A linear algebraic group G defined over a field k is called special if every G-torsor over every field extension of k is trivial. In 1958 Grothendieck classified special groups in the case where the base field is algebraically closed. In…

In this article, we classify disconnected reductive groups over an algebraically closed field with a few caveats. Internal parts of our result are both a classification of finite groups and a classification of integral representations of a…

We provide the Krull-Remak-Schmidt decomposition of group algebras of the form $k[G]$ where $k$ is a field, which includes fields with prime characteristic, and $G$ a finite abelian group. We achieved this by studying the geometric…

Let $G$ be a connected reductive algebraic group. Let $\mathcal{E}\rightarrow \mathcal{B}$ be a principal $G\times G$-bundle and $X$ be a regular compactification of $G$. We describe the Grothendieck ring of the associated fibre bundle…

Let $G$ be a complex, linear algebraic group acting on an algebraic space $X$. The purpose of this paper is to prove a Riemann-Roch theorem (Theorem 5.3) which gives a description of the completion of the equivariant Grothendieck group…

If T is an algebraic torus defined over a discretely valued field K with perfect residue field k, we relate the K-cohomology of T to the k-cohomology of certain objects associated to T. When k has cohomological dimension <= 1, our results…

The existence of closed orbits of real algebraic groups on real algebraic varieties is established. As an application, it is shown that if G is a real reductive linear group with Iwasawa decomposition G= KAN, then every unipotent subgroup…

The existence of closed orbits of real algebraic groups on certain real algebraic spaces is established. As an application it is shown that if $G$ is a real reductive group with Iwasawa decomposition $G=KAN$, then all unipotent subgroups of…

Let $A$ be a C*-algebra, $J \subset A$ a C*-subalgebra, and let $B$ be a stable C*-algebra. Under modest assumptions we organize invertible C*-extensions of $A$ by $B$ that are trivial when restricted onto $J$ to become a group…

We generalize the concept of rigid inner forms, defined by Kaletha in [Kal16], to the setting of a local function field $F$ in order state the local Langlands conjectures for arbitrary connected reductive groups over $F$. To do this, we…

In SGA3, Demazure and Grothendieck showed that if $G$ and $H$ are smooth affine group schemes over a scheme $S$ and $G$ is reductive, then the functor of $S$-homomorphism $G \to H$ is representable. In this paper we extend this result to…

Let G be a reductive group over an algebraically closed field k of separably good characteristic p>0 for G. Under these assumptions a Springer isomorphism from the reduced nilpotent scheme of the Lie algebra of G to the reduced unipotent…

The purpose of this paper is construct an embedding of the C*-algebra of the Cartan motion group of a real reductive group G into the reduced C*-algebra of G itself. The embedding has a number of applications: we shall use it to…

Let $k$ be an algebraically closed field of characteristic $p$. Denote by $W(k)$ the ring of Witt vectors of $k$. Let $F$ denote a totally ramified finite extension of $W(k)[1/p]$ and $\mathcal{O}$ the its ring of integers. For a connected…

It is a classical result that the set $K\backslash G /B$ is finite, where $G$ is a reductive algebraic group over an algebraically closed field with characteristic not equal to two, $B$ is a Borel subgroup of $G$, and $K = G^{\theta}$ is…

We show that every Fell bundle B over a locally compact group G is "proper" in a sense recently introduced by Ng. Combining our results with those of Ng we show that if B satisfies the "approximation property" then it is amenable in the…

We define a reduction, called complete reduction, for the K and KO relations of the Hopf bundle over lens spaces introducing some numbers of interest to various theories of mathematics. Along the way, we make an interesting conjecture in…

Let $G$ be a simple linear algebraic group over an algebraically closed field $K$ of characteristic $p \geqslant 0$, let $H$ be a proper closed subgroup of $G$ and let $V$ be a nontrivial finite dimensional irreducible rational $KG$-module.…

Let $G$ be a connected reductive algebraic group defined over an algebraically closed field $k$. The aim of this paper is to present a method to find triples $(G,M,H)$ with the following three properties. Property 1: $G$ is simple and $k$…

Let $V$ be a finite-dimensional real vector space and $K$ a compact simple Lie group with Lie algebra $\mathfrak{k}$. Consider the Fr\'echet-Lie group $G := J_0^\infty(V; K)$ of $\infty$-jets at $0 \in V$ of smooth maps $V \to K$, with Lie…