Related papers: Small principal series and exceptional duality for…
An elementary theory of strict $\infty $-categories with application to concrete duality is given. New examples of first and second order concrete duality are presented.
We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results…
Finite group theorists have established many formulas that express interesting properties of a finite group in terms of sums of characters of the group. An obstacle to applying these formulas is lack of control over the dimensions of…
The aim of this paper is to present a complete description of the structure of finite subsets with small doubling property in ordered nilpotent groups of class 2.
We define the notion of a minimal affinization of an irreducible representation of $U_q(g)$. We prove that minimal affinizations exist and establish their uniqueness in the rank 2 case.
The aim of this note (as well as of the course itself) is to give a largely self-contained proof of two of the main results in the field of low-rank matrix recovery. This field aims for identification of low-rank matrices from only limited…
This paper shows that the six classes of PPTs can be put into two groups. Autocorrelation and cross-correlation functions of the six classes derived from the gaps between each class type have been computed. It is shown that Classes A and D…
We show how to attach to any stratum of a reductive group a (small) finite group. We also show that in the simply laced case the set of strata is in bijection with a subset of the set of almost special representations of the Weyl group.…
The main result of this paper is the classification of the real irreducible representations of compact Lie groups with vanishing homogeneity rank.
We begin a systematic study of unitary representations of minimal $W$-algebras. In particular, we classify unitary minimal $W$-algebras and make substantial progress in classification of their unitary irreducible highest weight modules. We…
Ideal series of semigroups play an important role in the examination of semigroups which have proper two-sided ideals. But the corresponding theorems cannot be used when left simple (or right simple or simple) semigroups are considered. So…
Many real-world complex networks actually have a bipartite nature: their nodes may be separated into two classes, the links being between nodes of different classes only. Despite this, and despite the fact that many ad-hoc tools have been…
We investigate classifications of quasitrivial semigroups defined by certain equivalence relations. The subclass of quasitrivial semigroups that preserve a given total ordering is also investigated. In the special case of finite semigroups,…
We consider the restriction and induction of representations between a covering group and its derived subgroup, both on the representation-theoretic side and the L-parameter side. In particular, restriction of a genuine principal series is…
It is shown how a selection of prominent results in singularity theory and differential geometry can be deduced from one theorem, the Rank Theorem for maps between spaces of power series.
The first half of this dissertation reviews the basic notion of vector-valued modular forms and its connection to differential equations. The main purpose of the dissertation is to classify spaces of vector-valued modular forms associated…
We give an elementary description of $2$-categories $\mathbf{Cat}\left(\mathcal{E}\right)$ of internal categories, functors and natural transformations, where $\mathcal{E}$ is a category modelling Lawvere's elementary theory of the category…
In this paper, we extend the work in "Morita's Theory for the Symplectic Groups" to split reductive groups. We construct and study the holomorphic discrete series representation and the principal series representation of a split reductive…
The simple symplectic triple systems over the real numbers are classified up to isomorphism, and linear models of all of them are provided. Besides the split cases, one for each complex simple Lie algebra, there are two kinds of non-split…
We propose an algebraic and a geometric classification of euclidean isodual lattices of fixed rank. First, we prove that these lattices are distribued according to a finite number of algebraic types. Second, we show that they are…