Related papers: Computational Bounds for Doing Harmonic Analysis o…
In this paper we prove new lower bounds for the maximal size of permutation codes by connecting the theory of permutation codes with the theory of linear block codes. More specifically, using the columns of a parity check matrix of an…
We present a development in the computational suite for the study of $N_\infty$ operads for a finite group $G$. This progress is achieved using the simple yet powerful observation that Rubin's generation algorithm can be interpreted as a…
A conjecture of De Concini Kac and Procesi provides a bound on the minimal possible dimension of an irreducible module for quantized enveloping algebras at an odd root of unity. We pose the problem of the existence of modules whose…
Band structure for a crystal generally consists of connected components in energy-momentum space, known as band complexes. Here, we explore a fundamental aspect regarding the maximal number of bands that can be accommodated in a single band…
We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean space. These theorems extend the linear programming bounds…
We present lower bounds for the orbit length of reduction modulo primes of parametric polynomial dynamical systems defined over the integers, under a suitable hypothesis on its set of preperiodic points over $\mathbb C$. Applying recent…
In this paper, we study harmonic analysis on finite homogeneous spaces whose associated permutation representation decomposes with multiplicity. After a careful look at Frobenius reciprocity and transitivity of induction, and the…
Combined-resolution simulations are an effective way to study molecular properties across a range of length- and time-scales. These simulations can benefit from adaptive boundaries that allow the high-resolution region to adapt (change size…
We study an abstract setting for cutting planes for integer programming called the infinite group problem. In this abstraction, cutting planes are computed via cut generating function that act on the simplex tableau. In this function space,…
This paper presents a novel formulation and solution of orbit determination over finite time horizons as a learning problem. We present an approach to orbit determination under very broad conditions that are satisfied for n-body problems.…
The irreducible modules for the parafermion vertex operator algebra associated to any finite dimensional Lie algebra and any positive integer are identified, the quantum dimensions are computed and the fusion rules are determined.
The purpose of this article is to describe and characterize the limit distributions of translates of a bounded open "piece of orbit" of a reductive subgroup on a space of S-arithmetic lattices. This is accomplished under a mild assumption…
From celestial mechanics to quantum theory of atoms and molecules, perturbation theory has played a central role in natural sciences. Particularly in quantum mechanics, the amount of information needed for specifying the state of a…
Permutation modules play an important role in the representation theory of the symmetric group. Hartmann and Paget defined permutation modules for non-degenerate Brauer algebras. We generalise their construction to a wider class of…
We describe rules to simplify quantum circuits at their boundaries, i.e. at state preparation and measurement. There, any strictly incoherent operation may be pushed into a pre- or post-processing of classical data. The rules can greatly…
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
We apply the orbit method to obtain formula for multiplicities of certain representations of unipotent groups over the finite field.
Consider the representations of an algebraic group G. In general, polynomial invariant functions may fail to separate orbits. The invariant subring may not be finitely generated, or the number and complexity of the generators may grow…
We prove that, up to adding a complement, every modular representation of a finite group admits a finite resolution by permutation modules.
In this paper we study harmonic analysis operators in Dunkl settings associated with finite reflection groups on Euclidean spaces. We consider maximal operators, Littlewood-Paley functions, $\rho$-variation and oscillation operators…