Related papers: Integrity of ghosts
This paper contains an exposition of the theory of character sheaves for reductive groups and some attempts to extend it to other cases: unipotent groups, reductive groups modulo the unipotent radical of a parabolic.
We enumerate generalizations of the superintegrability property $<character>\ \sim {\rm character}$ and illuminate possible general structures behind them. We collect variations of original formulas available up to date and emphasize the…
The k-regular sequences exhibit a self-similar behaviour between powers of k. One way to study this self-similarity is to attempt to describe the limiting shape of the sequence using measures, which results in an object which we call the…
We study the symmetry properties of autonomous integrating factors from an algebraic point of view. The symmetries are delineated for the resulting integrals treated as equations and symmetries of the integrals treated as functions or…
It is shown how to sew string vertices with ghosts at tree level in order to produce new tree vertices using the Group Theoretic approach to String Theory. It is then verified the BRST invariance of the sewn vertex and shown that it has the…
This text is a survey on symmetric matrices. It serves as a script for a module to be taught at university.
We study several closely related invariants of the group algebra $kG$ of a finite group. The basic invariant is the ghost number, which measures the failure of the generating hypothesis and involves finding non-trivial composites of maps…
We discuss the use of methods coming from integrable systems to study problems of enumerative and algebraic combinatorics, and develop two examples: the enumeration of Alternating Sign Matrices and related combinatorial objects, and the…
We give an explicit expression of the normalized characters of the symmetric group in terms of the contents of the partition labelling the representation.
We study the differential geometric properties of the manifold of non-singular symmetric real matrices endowed with the trace metric; in case of positive definite matrices we describe the full group of isometries
For a Lie algebra L over an algebraically closed field of non-zero characteristic, every finite-dimensional L-module can be decomposed into a direct sum of submodules such that all composition factors of a summand have the same character.…
We present a framework for characterizing injectivity of classes of maps (on cosets of a linear subspace) by injectivity of classes of matrices. Using our formalism, we characterize injectivity of several classes of maps, including…
This paper defines and develops cycle indices for the finite classical groups. These tools are then applied to study properties of a random matrix chosen uniformly from one of these groups. Properties studied by this technique will include…
We find explicitly the generating functions of the multiplicities in the pure and mixed trace cocharacter sequences of two $4\times 4$ matrices over a field of characteristic 0. We determine the asymptotic behavior of the multiplicities and…
Computational ghost imaging relies on the decomposition of an image into patterns that are summed together with weights that measure the overlap of each pattern with the scene being imaged. These tasks rely on a computer. Here we…
The combination of the group ring setting with the methods of character theory allows an elegant and powerful analysis of various combinatorial structures, via their character sums. These combinatorial structures include difference sets,…
We describe isomorphisms of groups of several periodic infinite matrices and isomorphisms of groups of invertible elements of unital locally matrix algebras.
We give a new formula for the values of an irreducible character of the symmetric group S_n indexed by a partition of rectangular shape. Some observations and a conjecture are given concerning a generalization to arbitrary shapes.
Fourier analysis of ghost imaging (FAGI) is proposed in this paper to analyze the properties of ghost imaging with thermal light sources. This new theory is compatible with the general correlation theory of intensity fluctuation and could…
The characteristic polynomials of the adjacency matrix of line graphs of caterpillars and then the characteristic polynomials of their Laplacian or signless Laplacian matrices are characterized, using recursive formulas. Furthermore, the…