Related papers: Correspondances de Howe pour les groupes des simil…

In this note on coarse geometry we revisit coarse homotopy. We prove that coarse homotopy indeed is an equivalence relation, and this in the most general context of abstract coarse structures. We introduce (in a geometric way) coarse…

Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been investigated in the literature recently. We study Hom-structures from the point of view of monoidal categories; in particular, we introduce a symmetric monoidal…

This paper gives a $p$-adic analogue of the Mackey theory, which relates representations of a group of type $G=H\times_{t} A $ to systems of imprimitivity.

We establish classical and categorical Howe dualities between the Lie superalgebras $\mathfrak{p}(m)$ and $\mathfrak{p}(n)$, for $m,n \geq 1$. We also describe a presentation via generators and relations as well as a Kostant…

We connect work done by Enochs, Rada and Hill in module approximation theory with work undertaken by several group theorists and algebraic topologists in the context of homotopical localization and cellularization of spaces. This allows one…

In this text we apply the methods of Hodge theory for isolated hypersurface singularities to define a signature for the Grothendieck residue pairing of these singularities.

In this paper, we define equivariant evaluation subgroups of the higher Rhodes groups and study their relations with Gottlieb-Fox groups.

This is an exposition of our work on the canonical models of representations of Hardy algebras associated with $W^*$-correspondences. It generalizes the model theory of Sz.-Nagy and Foias and the work of Popescu on models of row…

Let G be a finite group and p a prime dividing its order. We define new collections of p-subgroups of G. We study the homotopy relations among them and with the standard collections of p-subgroups. We determine their ampleness and sharpness…

We explicitly determine the theta correspondences for $\GSp_4$ and orthogonal similitude groups associated to various quadratic spaces of rank $4$ and $6$. The results are needed in our proof of the local Langlands correspondence for…

Let $H$ be a Hopf algebra, and $A$ an $H$-Galois extension. We investigate $H$-Morita autoequivalences of $A$, introduce the concept of $H$-Picard group, and we establish an exact sequence linking the $H$-Picard group of $A$ and the Picard…

We calculate certain homotopy groups of the moduli spaces for representations of a compact oriented surface in the Lie groups GL(n,C) and U(p,q). Our approach relies on the interpretation of these representations in terms of Higgs bundles…

We use Janelidze's Categorical Galois Theory to extend Brown and Ellis's higher Hopf formulae for homology of groups to arbitrary semi-abelian monadic categories. Given such a category A and a chosen Birkhoff subcategory B of A, thus we…

Butz and Moerdijk famously showed that every (Grothendieck) topos with enough points is equivalent to the category of sheaves on some topological groupoid. We give an alternative, more algebraic construction in the special case of a topos…

We show that s-convergence of graph sequences is equivalent to the convergence of certain compact sets, called shapes, of Borel probability measures. This result is analogous to the characterization of graphon convergence (with respect to…

We construct the Arthur packets for symplectic and even orthogonal similitude groups over a $p$-adic field and show that they are stable and satisfy the twisted endoscopic character relations.

Hughes defined a class of groups that act as local similarities on compact ultrametric spaces. Guba and Sapir had previously defined braided diagram groups over semigroup presentations. The two classes of groups share some common…

We give an explicit description of the homomorphism group H_n(p) of a strong type p in any stable theory under the assumption that for every non-forking extension q of p the groups H_i(q) are trivial for i at least 2 but less than n. The…

We describe the relation of $r$-similarity and finite-order invariants on the homotopy set $[S^1,Y]=\pi_1(Y)$.

Let $K$ be a mixed characteristic complete discrete valuation field with residue field admitting a finite $p$-basis, and let $G_K$ be the Galois group. Inspired by Liu and Zhu's construction of $p$-adic Simpson and Riemann-Hilbert…