相关论文: Equivalent definitions of Arthur packets for real …

Attack Trees (ATs) are a widely used tool for security analysis. ATs can be employed in quantitative security analysis through metrics, which assign a security value to an AT. Many different AT metrics exist, and there exist multiple…

In a recent paper I defined a new basis for the Grothendieck group of unipotent representations of an almost simple Chevalley group over a finite field. The definition for classical types was different from that for exceptional types. In…

For classical groups we show the isomorphism of the Knapp-Stein $R$-group, which describes the structure of parabolically induced representations, and the Arthur $R$-group of the parameter associated to the inducing representation by the…

Broadly speaking, there are two kinds of semantics-aware assistant systems for mathematics: proof assistants express the semantic in logic and emphasize deduction, and computer algebra systems express the semantics in programming languages…

Given a right-angled Artin group $G$ with finite outer automorphism group, we determine which right-angled Artin groups are measure equivalent (or orbit equivalent) to $G$.

We introduce the notion of continuous orbit equivalence for partial dynamical systems, and give an equivalent characterization in terms of Cartan-isomorphisms for partial C*-crossed products. Both graph C*-algebras and semigroup C*-algebras…

This paper deals with the Langlands' classification for discrete series of unitary quasi-split p-adic groups. We show that such a classification follows from Arthur's work on the simple trace formula which we can use now thanks to…

The classifying spaces of handlebody groups form a modular operad. Algebras over the handlebody operad yield systems of representations of handlebody groups that are compatible with gluing. We prove that algebras over the modular operad of…

In \cite[Section 5, p.32]{Arnold-1998}, Arnold writes: "Classification of singularities of curves can be interpreted in dual terms as a description of 'co-artin' subalgebras of finite co-dimension in the algebra of formal series in a single…

The local intertwining relation is an identity that gives precise information about the action of normalized intertwining operators on parabolically induced representations. We prove several instances of the local intertwining relation for…

Two matrices $A$ and $B$ are called unitary (resp. orthogonal) equivalent if $AU=VB$ for two unitary (resp. orthogonal) matrices $U$ and $V$. Using trace identities, criteria are given for simultaneous unitary, orthogonal or complex…

Special matchings are purely combinatorial objects associated with a partially ordered set, which have applications in Coxeter group theory. We provide an explicit characterization and a complete classification of all special matchings of…

These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond…

We study the complexity of the $KK$-equivalence relation on unital $C^*$-algebras, in the sense of descriptive set theory. We prove that $KK$-equivalence is analytic, which in turn shows that the set of separable $C^*$-algebras satisfying…

A group-category is an additively semisimple category with a monoidal product structure in which the simple objects are invertible. For example in the category of representations of a group, 1-dimensional representations are the invertible…

The semigroups of unital extensions of separable $C^\ast$-algebras come in two flavours: a strong and a weak version. By the unital $\mathrm{Ext}$-groups, we mean the groups of invertible elements in these semigroups. We use the unital…

A core challenge of Monte Carlo Tree Search (MCTS) is its sample efficiency, which can be improved by grouping state-action pairs and using their aggregate statistics instead of single-node statistics. On the Go Abstractions in Upper…

We introduce a new geometric tool for analyzing groups of finite automata. To each finite automaton we associate a square complex. The square complex is covered by a product of two trees iff the automaton is bi-reversible. Using this method…

We define varieties of algebras for an arbitrary endofunctor on a cocomplete category using pairs of natural transformations. This approach is proved to be equivalent to the one of equational classes defined by equation arrows. Free…

A unitary operator which relates the system of a particle in a linear potential with time-dependent parameters to that of a free particle, has been given. This operator, closely related to the one which is responsible for the existence of…