Related papers: On Foulkes characters
By generalizing Frobenius' polynomial method to good partition algebra, we will develop new character theories for a finite group $G$. A uniform defining equations are derived for these kinds of character theories. The new character…
Properties of higher characters are developed and applied to symmetric products and Frobenius algebras. A `constructive' proof of the Gel'fand-Kolmogorov theorem is given. Generalisations of that theorem and the Nullstellensatz to symmetric…
We study connections between the topology of generic character varieties of fundamental groups of punctured Riemann surfaces, Macdonald polynomials, quiver representations, Hilbert schemes on surfaces, modular forms and multiplicities in…
For a block B of a finite group G there are well-known orthogonality relations for the generalized decomposition numbers. We refine these relations by expressing the generalized decomposition numbers with respect to an integral basis of a…
Some general connections between martingales and character ratios of finite groups are developed. As an application we sharpen the convergence rate in a central limit theorem for the character ratio of a random representation of the…
The text deals with generalizations of the Markoff equation in number theory, arising from continued fractions. It gives the method for the complete resolution of such new equations, and their interpretation in algebra and algebraic…
We count points over a finite field on wild character varieties of Riemann surfaces for singularities with regular semisimple leading term. The new feature in our counting formulas is the appearance of characters of Yokonuma-Hecke algebras.…
Given a pair of modular forms with complex multiplication by distinct imaginary quadratic fields, the four dimensional Galois representation associated to their Rankin--Selberg convolution is induced from a character over an imaginary…
In an earlier paper [1] it was shown that the Frobenius compound characters for the symmetric groups are related to the irreducible characters by a linear relation that involves a unitriagular coupling matrix that gives the Frobenius…
In this Colloqium Lecture (by one of the authors (D.S)) a thorough presentation of the authors' research on the subjects, stated in the title, is given. By quite laborious mathematics it is explained how one can handle systems in which each…
Our approach to higher order Fourier analysis is to study the ultra product of finite (or compact) Abelian groups on which a new algebraic theory appears. This theory has consequences on finite (or compact) groups usually in the form of…
We introduce a generic framework to provide bounds related to the pair correlation of sequences belonging to a wide class. We consider analogues of Montgomery's form factor for zeros of the Riemann zeta function in the case of arbitrary…
In the paper [1] (arXiv:math/0408333) the authors discuss two possible definitions of the relative Cheeger-Simons characters, the second one fitting into a long exact sequence. Here we relate that picture to the one of the relative Deligne…
We determine the rationality properties of unipotent characters of finite reductive groups arising as fixed points of disconnected reductive groups under a Frobenius map. In the proof we use realisations of characters in $\ell$-adic…
We construct a new family of homomorphisms from Specht modules into Foulkes modules for the symmetric group. These homomorphisms are used to give a combinatorial description of the minimal partitions (in the dominance order) which label…
We give new evidences to the fact that the structure of a solvable group can be controlled by irreducible monomial characters. In particular we inspect the role of monomial characters in Isaacs-Navarro-Wolf's conjecture and in Gluck's…
A family of new algebraic Poisson varieties will be constructed, generalising the complex character varieties of Riemann surfaces. Then the well-known (Poisson) mapping class group actions on the character varieties will be generalised.
We study algebraic isomonodromic deformations of flat logarithmic connections on the Riemann sphere with $n\geq 4$ poles, for arbitrary rank. We introduce a natural property of algebraizability for the germ of universal deformation of such…
A finitely presented group F is called flawed if Hom(F,G)//G deformation retracts onto its subspace Hom(F,K)/K for reductive affine algebraic groups G and maximal compact subgroups K in G. After discussing generalities concerning flawed…
We show how the theory of characters can be used to analyse an anomaly corresponding to chiral fermions carrying an arbitrary representation of a gauge group that is finite, but otherwise arbitrary. By way of example, we do this for some…