Related papers: An inductive machinery for representations of cate…

In this work, we show that extending the standard description of space-time symmetries from groups of isometries to the more flexible framework of kinematical groupoids allows for the extension of Wigner's program to curved space-times. We…

In this paper, we introduce the notions of motivic representation stability that is an algebraic counterpart of the notion of representation stability. In the process, we also introduce the notion of motivic decomposition for varieties…

We prove an induction theorem for the higher algebraic K-groups of group algebras $kG$ of finite groups $G$ over characteristic $p$ finite fields $k$. For a certain class of finite groups, which we call $p$-isolated, this reduces…

Using the Nakayama functor, we construct an equivalence from a Serre quotient category of a category of finitely generated modules to a category of finite-dimensional modules. We then apply this result to the categories FI$_G$ and VI$_q$,…

We examine various categorical structures that can and cannot be constructed. We show that total computable functions can be mimicked by constructible functors. More generally, whatever can be done by a Turing machine can be constructed by…

Any refinement system (= functor) has a fully faithful representation in the refinement system of presheaves, by interpreting types as relative slice categories, and refinement types as presheaves over those categories. Motivated by an…

We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a…

We give a presentation of Feynman categories from a representation--theoretical viewpoint. Feynman categories are a special type of monoidal categories and their representations are monoidal functors. They can be viewed as a far reaching…

A major problem in system identification is the incorporation of prior knowledge about the physical properties of the given system, such as stability, positivity and passivity. In this paper, we present first steps towards tackling this…

We extend the discussion of projective group representations in quaternionic Hilbert space which was given in our recent book. The associativity condition for quaternionic projective representations is formulated in terms of unitary…

Turing machines and spin models share a notion of universality according to which some simulate all others. Is there a theory of universality that captures this notion? We set up a categorical framework for universality which includes as…

In this paper we study representation theory of the category FI$^m$ introduced by Gadish which is a product of copies of the category FI, and show that quite a few interesting representational and homological properties of FI can be…

Several advances have extended the power and versatility of coherent state theory to the extent that it has become a vital tool in the representation theory of Lie groups and their Lie algebras. Representative applications are reviewed and…

We consider a group SO(2n+1) over a p-adic field, and tempered irreducible representations of this group, of unipotent reduction. We use the construction due to Lusztig of these representations. In an old paper with Moeglin, we have defined…

We introduce enumerative invariants $F_{g,n}$ $(g\geq0$, $n \geq 1)$ associated to a cyclic $A_\infty$ algebra and a splitting of its non-commutative Hodge filtration. These invariants are defined by explicitly computable Feynman sums, and…

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 the $F$-points of a connected reductive group over a non-archimedean local field $F$ of residue characteristic $p$ and $R$ be a commutative ring. Let $P=LU$ be a parabolic subgroup of $G$ and $Q$ be a parabolic subgroup of $G$…

In this work we extend the Mackey's theory of induced unitary representations on a wide class of Krein-isometric induced representations in Krein spaces. The subgroup theorem and the Kronecker product theorem are shown to be valid for the…

Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…

We show that the class of representable substitution algebras is characterized by a set of universal first order sentences. In addition, it is shown that a necessary and sufficient condition for a substitution algebra to be representable is…