Related papers: Generalizations of some integrals over the unitary…
In this investigation of character tables of finite groups we study basic sets and associated representation theoretic data for complementary sets of conjugacy classes. For the symmetric groups we find unexpected properties of characters on…
We generalise well-known integrals of Ingham-Siegel and Fisher-Hartwig type over the unitary group $U(N)$ with respect to Haar measure, for finite $N$ and including fixed external matrices. When depending only on the eigenvalues of the…
Concise review of the basic properties of unitary matrix integrals. They are studied with the help of the three matrix models: the ordinary unitary model, Brezin-Gross-Witten model and the Harish-Charndra-Itzykson-Zuber model. Especial…
We show that randomly choosing the matrices in a completely positive map from the unitary group gives a quantum expander. We consider Hermitian and non-Hermitian cases, and we provide asymptotically tight bounds in the Hermitian case on the…
We consider generalized one-matrix models in which external fields allow control over the coordination numbers on both the original and dual lattices. We rederive in a simple fashion a character expansion formula for these models originally…
We show the existence of and explicitly construct generic polynomials for various groups, over fields of positive characteristic. The methods we develop apply to a broad class of connected linear algebraic groups defined over finite fields…
The weight systems of finite-dimensional representations of complex, simple Lie algebras exhibit patterns beyond Weyl-group symmetry. These patterns occur because weight systems can be decomposed into lattice polytopes in a natural way.…
We describe the "generic" part of the character ring of general linear groups over a finite field in terms of quiver representations.
We extend the notion of generalized unitarity cuts to accommodate loop integrals with higher powers of propagators. Such integrals frequently arise in for example integration-by-parts identities, Schwinger parametrizations and Mellin-Barnes…
The theory of algebraic extensions of Banach algebras is well established, and there are many constructions which yield interesting extensions. In particular, Cole's method for extending uniform algebras by adding square roots of functions…
Zalcman's Lemma makes significant applications in normal families, complex dynamics and related problems in complex analysis. In the present paper, we are devoted to generalizing the classical Zalcman's lemma to complex Lie groups by means…
For autonomous Tonelli systems on $\R^n$, we develop an intrinsic proof of the existence of generalized characteristics using sup-convolutions. This approach, together with convexity estimates for the fundamental solution, leads to new…
Generalized numberings are an extension of Ershov's notion of numbering, based on partial combinatory algebra (pca) instead of the natural numbers. We study various algebraic properties of generalized numberings, relating properties of the…
The study of the relation between Lie algebras and groups, and especially the derivation of new algebras from them, is a problem of great interest in mathematics and physics, because finding a new Lie group from an already known one also…
Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…
Even with the introduction of supercharacter theories, the representation theory of many unipotent groups remains mysterious. This paper constructs a family of supercharacter theories for normal pattern groups in a way that exhibit many of…
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 study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…
This is a survey of the use of Fourier analysis in additive combinatorics, with a particular focus on situations where it cannot be straightforwardly applied, but needs to be generalized first. Sometimes very satisfactory generalizations…
We construct a very general family of characteristic functions describing Random Matrix Ensembles (RME) having a global unitary invariance, and containing an arbitrary, one-variable probability measure which we characterize by a `spread…