Related papers: Representability of derived stacks

We study extension properties for morphisms of stacks of bundles for group algebraic spaces. Applications are a short proof of the classification of bundles on the projective line for smooth geometrically reductive groups and the existence…

It is generally believed (and for the most part is probably true) that Lie theory, in contrast to the characteristic zero case, is insufficient to tackle the representation theory of algebraic groups over prime characteristic fields.…

For representation by partial functions in the signature with intersection, composition and antidomain, we show that a representation is meet complete if and only if it is join complete. We show that a representation is complete if and only…

This note states and proves a representation theorem for regular quantity functions, based on the theory of quantity spaces, thereby giving a new perspective on dimensional analysis and the classical $\pi$ theorem.

In this paper we present the notion of ``Deligne localized functors'', an avatar of the derived functors, whose definition is inspired by Deligne in [SGA 4,XVII]. Their definition involves the notions of Ind and Pro categories, they always…

In this paper, we construct in characteristic zero a derived foliation on derived mapping stacks $\underline{\mathbf{Map}}_S(X,Y)$, for $S$ a base derived stack, $X$ a proper schematic, flat, and local complete intersection derived stack…

According to Letourmy and Vendramin, a representation of a skew brace is a pair of representations on the same vector space, one for the additive group and the other for the multiplicative group, that satisfies a certain compatibility…

There is a large ongoing scientific effort in mechanistic interpretability to map embeddings and internal representations of AI systems into human-understandable concepts. A key element of this effort is the linear representation…

Motivated by the study of the interrelation between functorial and algebraic quantum field theory, we point out that on any locally trivial bundle of compact groups, representations up to homotopy are enough to separate points by means of…

We establish a form of the h-principle for the existence of foliations quasi-complementary to a given one; the same methods also provide a proof of the classical Mather-Thurston theorem.

Linearity allows several versions of reality to simultaneously exist in the state vector. But it implies that there is no interaction between versions, and that there will never be perception of more than one version. It also implies, in…

Let G be a reductive algebraic group over a field k and let B be a Borel subgroup in G. We demonstrate how a number of results on the cohomology of line bundles on the flag manifold G/B have had interesting consequences in the…

Derived functors (or Zuckerman functors) play a very important role in the study of unitary representations of real reductive groups. These functors are usually applied on highest weight modules in the so-called good range and the theory is…

Let X be a proper scheme over a field k which satisfies Serre's condition S2 and G a reductive group over k. We prove that the functor of principal G-bundles defined away from a non-fixed closed subset in X of codimension at least 3, is an…

Using representation theory techniques we prove that various spaces of derivations or one-sided multipliers over certain operator algebras are reflexive. A sample result: any bounded local derivation (local left multiplier) on an…

In the two parts of this paper we solve a problem of De Rham, proving that Reidemeister torsion invariants determine topological equivalence of linear G-representations, for G a finite cyclic group. Methods in controlled K-theory and…

Given a minuscule representation of a simple Lie algebra, we find an algebraic model for the action of a regular element and show that these models can be glued together over the adjoint quotient, viewed as the set of all regular conjugacy…

Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness. Here we study approximate representations of finite groups:…

We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…

We prove in significant generality the (almost-)representability of the Picard functor when restricted to smooth test schemes. The novelty lies in the fact that we prove such (almost-)representability beyond the proper setting.