Related papers: Supercharacters, exponential sums, and the uncerta…

In this article we extend independent results of Lusztig and H\'ezard concerning the existence of irreducible characters of finite reductive groups, (defined in good characteristic and arising from simple algebraic groups), satisfying a…

We obtain new bounds on some trilinear and quadrilinear character sums, which are non-trivial starting from very short ranges of the variables. An application to an apparently new problem on oscillations of characters on differences between…

Given a discrete group $G$ with a finite model for $\underline{E}G$, we study $K(n)^*(BG)$ and $E^*(BG)$, where $K(n)$ is the $n$-th Morava $K$-theory for a given prime and $E$ is the height $n$ Morava $E$-theory. In particular we…

We introduce the characteristic numbers and the chromatic polynomial of a tensor. Our approach generalizes and unifies the chromatic polynomial of a graph and of a matroid, characteristic numbers of quadrics in Schubert calculus, Betti…

Average of exponential ${\rm Tr}_R e^X$, i.e. of a group rather than an algebra character, in Gaussian matrix model is known to be an amusing generalization of Schur polynomial, where time variables are substituted by traces of products of…

We define and study supercharacters of the classical finite unipotent groups of symplectic and orthogonal types (over any finite field of odd characteristic). We show how supercharacters for groups of those types can be obtained by…

John Holte [16] introduced a family of "amazing matrices" which give the transition probabilities of "carries" when adding a list of numbers. It was subsequently shown that these same matrices arise in the combinatorics of the Veronese…

We consider a generalisation of the classical Lehmer problem about the distribution of modular inverses in arithmetic progression, introduced by E. Alkan, F. Stan and A. Zaharescu. Using bounds of sums of multiplicative characters instead…

We study a class of newly-introduced CFTs associated with even quadratic forms of general signature, which we call generalized Narain theories. We first summarize the properties of these theories. We then consider orbifolds of these…

Recently, Granville and Soundararajan have made fundamental breakthroughs in the study of character sums. Building on their work and using estimates on short character sums developed by Graham-Ringrose and Iwaniec, we improve the…

Analytic number theorists usually seek to show that sequences which appear naturally in arithmetic are ``well-distributed'' in some appropriate sense. In various discrepancy problems, combinatorics researchers have analyzed limitations to…

In 1837, Dirichlet proved that there are infinitely many primes in any arithmetic progression in which the terms do not all share a common factor. We survey implicit and explicit uses of Dirichlet characters in presentations of Dirichlet's…

A classical theorem of John Thompson on character degrees asserts that if the degree of every ordinary irreducible character of a finite group $G$ is 1 or divisible by a prime $p$, then $G$ has a normal $p$-complement. We obtain a…

An elementary approach is shown which derives the values of the Gauss sums over $\mathbb F_{p^r}$, $p$ odd, of a cubic character without using Davenport-Hasse's theorem. New links between Gauss sums over different field extensions are shown…

Finding upper bounds for character ratios is a fundamental problem in asymptotic group theory. Previous bounds in the symmetric group have led to remarkable applications in unexpected domains. The existing approaches predominantly relied on…

We introduce certain relative differential characters which we call Cheeger-Chern-Simons characters. These combine the well-known Cheeger-Simons characters with Chern-Simons forms. In the same way as the Cheeger-Simons characters generalize…

The Euler-Poincar\'e characteristic of a finite-dimensional Lie algebra vanishes. If we want to extend this result to Lie superalgebras, we should deal with infinite sums. We observe that a suitable method of summation, which goes back to…

We continue investigating the superintegrability property of matrix models, i.e. factorization of the matrix model averages of characters. This paper focuses on the Gaussian Hermitian example, where the role of characters is played by the…

In this paper we first prove that every differential character can be represented by differential form with singularities. Then we lift the Gauss-Bonnet-Chern theorem for vector bundles to differential characters.

We introduce the notion of a diagram category and discuss its application to the invariant theory of classical groups and super groups, with some indications concerning extensions to quantum groups and quantum super groups. Tensor functors…