相关论文: Branching problems of unitary representations

In this paper we study branching laws for certain unitary representations. This is done on the smooth vectors via a version of the {\it period integrals}, studied in number theory, and also closely connected to the {\it symmetry-breaking…

A wide range of constraints can be compactly specified using automata or formal languages. In a sequence of recent papers, we have shown that an effective means to reason with such specifications is to decompose them into primitive…

The problem of simultaneous decomposition of binary forms as sums of powers of linear forms is studied. For generic forms the minimal number of linear forms needed is found and the space parametrizing all the possible decompositions is…

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…

In this paper we consider symmetric powers representation and exterior powers representation of finite groups, which generated by the representation which has finite dimension over the complex field. We calculate the multiplicity of…

There have been several attempts to extend the notion of conjugacy from groups to monoids. The aim of this paper is study the decidability and independence of conjugacy problems for three of these notions (which we will denote by $\sim_p$,…

Our work proposes a unified approach to three different topics in a general Riemannian setting: splitting theorems, symmetry results and overdetermined elliptic problems. By the existence of a stable solution to the semilinear equation…

One can embed arbitrarily many disjoint, non-parallel, non-boundary parallel, incompressible surfaces in any three manifold with at least one boundary component of genus two or greater [4]. This paper proves the contrasting, but not…

This survey addresses sampling discretization and its connections with other areas of mathematics. The survey concentrates on sampling discretization of norms of elements of finite-dimensional subspaces. We present here known results on…

Unfolding singular points in linear differential equations is a classical technique for studying the properties of irregular singularities by relating them to regular singularities. In this paper, we propose a general framework for…

Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…

We give a survey on the theory of representation-finite and certain minimal representation-infinite algebras.The main goals are the existence of multiplicative bases and of coverings with good properties. Both are attained via…

Is string theory uniquely determined by self-consistency? Causality and unitarity seemingly permit a multitude of putative deformations, at least at the level of two-to-two scattering. Motivated by this question, we initiate a systematic…

Classifications of irreducible components of the set of polynomial differential equations with a fixed degree and with at least one center singularity lead to some other new problems on Picard-Lefschetz theory and Brieskorn modules of…

Recent advances in our understanding of higher derived limits carry multiple implications in the fields of condensed and pyknotic mathematics, as well as for the study of strong homology. These implications are thematically diverse,…

We identify a decidable synthesis problem for a class of programs of unbounded size with conditionals and iteration that work over infinite data domains. The programs in our class use uninterpreted functions and relations, and abide by a…

The permutation matrices form a subgroup of $\text{GL}_n(\mathbb{C})$ that is isomorphic to the symmetric group $S_n$. Let $r_{\mu\lambda}$ denote the multiplicity of the irreducible representation $V_\mu$ of $S_n$, corresponding to a…

The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…

The problem of expressing a specific polynomial as the determinant of a square matrix of affine-linear forms arises from algebraic geometry, optimisation, complexity theory, and scientific computing. Motivated by recent developments in this…

We consider large uniform labeled random graphs in different classes with prescribed decorations in their modular decomposition. Our main result is the estimation of the number of copies of every graph as an induced subgraph. As a…