Related papers: Homogeneous spaces in tensor categories

Let $G/\Gamma$ be the quotient of a semisimple Lie group by an arithmetic lattice. We show that for reductive subgroups $H$ of $G$ that is large enough, the orbits of $H$ on $G/\Gamma$ intersect nontrivially with a fixed compact set. As a…

We show that a compact rigid balanced braided monoidal category with enough compact projective objects gives rise to a system of mapping class group representations compatible with the gluing along marked intervals. A motivation to consider…

Commutative Hilbertian Frobenius algebras are those commutative semi-group objects in the monoidal category of Hilbert spaces, for which the Hilbert adjoint of the multiplication satisfies the Frobenius compatibility relation, that is, this…

For certain contractible G-CW-complexes and F a family of subgroups of G, we construct a spectral sequence converging to the F-Bredon cohomology of G with E1-terms given by the F-Bredon cohomology of the stabilizer subgroups. As…

Let X=G/H be the quotient of a connected reductive algebraic C-group G defined over the field of complex numbers C by a finite subgroup H. We describe the topological fundamental group of the homogeneous space X, which is nonabelian when H…

A subgroup $H\leq G$ is said to be almost normal if every conjugate of $H$ is commensurable to $H$. If $H$ is almost normal, there is a well-defined quotient space $G/H$. We show that if a group $G$ has type $F_{n+1}$ and contains an almost…

Let $G$ be a complex connected reductive algebraic group and $G/B$ denote the flag variety of $G$. A $G$-homogeneous space $G/H$ is said to be {\it spherical} if $H$ acts on $G/B$ with finitely many orbits. A class of spherical homogeneous…

Let $G$ be a compact connected Lie group and $K$ a closed connected subgroup. Assume that the order of any torsion element in the integral cohomology of $G$ and $K$ is invertible in a given principal ideal domain $k$. It is known that in…

Let k be a global field. Let G be a connected linear algebraic k-group, assumed reductive when k is a function field. It follows from a result of a preprint by Bary-Soroker, Fehm and Petersen that when H is a smooth connected k-subgroup of…

A topological group $G$ is called extremely amenable if every continuous action of $G$ on a compact space has a fixed point. This concept is linked with geometry of high dimensions (concentration of measure). We show that a von Neumann…

We show that given a rigid C*-tensor category, there is an equivalence of categories between normalized irreducible Q-systems, also known as connected unitary Frobenius algebra objects, and compact connected W*-algebra objects. Although…

It is well known that if two finite groups have the same symmetric tensor categories of representations over C, then they are isomorphic. We study the following question: when do two finite groups G1,G2 have the same tensor categories of…

A reductive homogeneous space $G/H$ is always diffeomorphic to the normal bundle of an orbit of a maximal compact subgroup of $G$. We prove that if $G/H$ admits compact quotients, then the sphere bundle associated to this normal bundle is…

Let $FH$ be a Frobenius group with kernel $F$ and complement $H$, acting coprimely on the finite solvable group $G$ by automorphisms. We prove that if $C_{G}(H)$ is of Fitting length $n$ then the index of the $n$-th Fitting subgroup…

Let G be a complex reductive algebraic group. We study complete intersections in a spherical homogeneous space G/H defined by a generic collection of sections from G-invariant linear systems. Whenever nonempty, all such complete…

We show that any nonabelian free group $F$ of finite rank is homogeneous; that is for any tuples $\bar a$, $\bar b \in F^n$, having the same complete $n$-type, there exists an automorphism of $F$ which sends $\bar a$ to $\bar b$. We further…

Let $FH$ be a supersolvable Frobenius group with kernel $F$ and complement $H$. Suppose that a finite group $G$ admits $FH$ as a group of automorphisms in such a manner that $C_G(F)=1$ and $C_{G}(H)$ is nilpotent of class $c$. We show that…

In this paper we study the Plancherel formula for a new class of homogeneous spaces for real reductive Lie groups; these spaces are fibered over non-Riemannian symmetric spaces, and they exhibit a phenomenon of uniform infinite…

We prove that if $G$ is a noncompact connected real reductive linear Lie group, then any discrete subgroup of $G$ acting properly discontinuously and cocompactly on some homogeneous space $G/H$ of $G$ is quasi-isometrically embedded and…

We prove that every finite symmetric integral tensor category $\mathcal{C}$ with the Chevalley property over an algebraically closed field $k$ of characteristic $p>2$ admits a symmetric fiber functor to $\text{sVec}$. This proves Ostrik's…