Related papers: Geometric Conditions for Twisted O-Sphericity

The goal of this expository article, based on a lecture I gave at the 2016 ICRA, is to explain some recent applications of "categorical symmetries" in topology and algebraic geometry with an eye toward twisted commutative algebras as a…

We construct a gerbe over a complex reductive Lie group G attached to an invariant bilinear form on a maximal diagonalizable subalgebra which is Weyl group invariant and satisfies a parity condition. By restriction to a maximal compact…

We give a unified description of twisted forms of classical reductive groups schemes. Such group schemes are constructed from algebraic objects of finite rank, excluding some exceptions of small rank. These objects, augmented odd form…

Within the framework of supersymmetric quantum mechanics, we study the simplified version of potential algebra of shape invariance condition in k steps, where k is an arbitrary positive integer. The associated potential algebra is found to…

We investigate deformations of skew group algebras that arise from a finite cyclic group acting on a polynomial ring in positive characteristic, where characteristic divides the order of the group. We allow deformations which deform both…

This article introduces and studies the tight approximation property, a property of algebraic varieties defined over the function field of a complex or real curve that refines the weak approximation property (and the known cohomological…

Let $G$ be a group and let $V$ be an algebraic group over an algebraically closed field. We introduce algebraic group subshifts $\Sigma \subset V^G$ which generalize both the class of algebraic sofic subshifts of $V^G$ and the class of…

There were defined by R. Shwartz OGS for non-abelian groups, as an interesting generalization of the basis of finite abelian groups. The definition of OGS states that that every element of a group has a unique presentation as a product of…

We study homological multiplicities of spherical varieties of reductive group $G$ over a $p$-adic field $F$. Based on Bernstein's decomposition of the category of smooth representations of a $p$-adic group, we introduce a sheaf that…

Let G be a connected reductive linear algebraic group. We use geometric methods to investigate G-completely reducible subgroups of G, giving new criteria for G-complete reducibility. We show that a subgroup of G is G-completely reducible if…

Similarly to how the classical group ring isomorphism problem asks, for a commutative ring $R$, which information about a finite group $G$ is encoded in the group ring $RG$, the twisted group ring isomorphism problem asks which information…

We study universal groups for right-angled buildings. Inspired by Simon Smith's work on universal groups for trees, we explicitly allow local groups that are not necessarily finite nor transitive. We discuss various topological and…

We generalize results of P. Schneider and U. Stuhler for GL_l+1 to a reductive algebraic group G defined and split over a non-archimedean local field K. Following their lines, we prove that the generalized Steinberg representations of G…

There exists a multiplicative homomorphism from the braid group B to the Temperley-Lieb algebra TL. Moreover, the homomorphic images in TL of the simple elements form a basis for the vector space underlying TL. In analogy with the case of…

A group element is called generalized torsion if a finite product of its conjugates is equal to the identity. We show that in a finitely generated abelian-by-finite group, an element is generalized torsion if and only if its image in the…

Suppose that G is a finite, unitary reflection group acting on a complex vector space V and X is the fixed point subspace of an element of G. Define N to be the setwise stabilizer of X in G, Z to be the pointwise stabilizer, and C=N/Z. Then…

Let $G_\cpl$ be a connected complex reductive Lie group, and $G$ be a real form. Let $(\pi,V)$ be a finite-dimensional irreducible representation of $G$. Assume $(\pi,V)$ admits a $G$ invariant hermitian form. {In…

We state a theorem relating the ergodicity of the action of a given subgroup of the mapping class group of a surface on the character variety, to the asymptotic of its invariant subspaces through the Witten-Reshetikhin-Turaev…

The description of irreducible representations of a group G can be seen as a question in harmonic analysis; namely, decomposing a suitable space of functions on G into irreducibles for the action of G x G by left and right multiplication.…

Let $G$ be a symplectic or special orthogonal group, let $H$ be a connected reductive subgroup of $G$, and let $X$ be a flag variety of $G$. We classify all triples $(G,H,X)$ such that the natural action of $H$ on $X$ is spherical. For each…