Related papers: Multiplicative characters and Gaussian fluctuation…
We study the characteristic polynomials of both the Gaussian Orthogonal and Symplectic Ensembles. We show that for both ensembles, powers of the absolute value of the characteristic polynomials converge in law to Gaussian multiplicative…
For any element $g$ of compact reductive group $G$ we investigate the asymptotic behavior of its normalized irreducible character in the high-dimension limit, $\frac{\chi_\lambda(g)}{d_\lambda}$. We show that when $G$ is simple the limit…
One of the main features of eigenvalue matrix models is that the averages of characters are again characters, what can be considered as a far-going generalization of the Fourier transform property of Gaussian exponential. This is true for…
If G is a finite group and H is a subgroup of G, we characterize when restriction of Brauer characters from G to H is injective.
In this article, we study complex Gaussian multiplicative chaos. More precisely, we study the renormalization theory and the limit of the exponential of a complex log-correlated Gaussian field in all dimensions (including Gaussian Free…
Gaussian elimination is used in special linear groups to solve the word problem. In this paper, we extend Gaussian elimination to unitary groups. These algorithms have an application in building a public-key cryptosystem, we demonstrate…
We use character theory of finite groups of Lie type to establish new results on representation varieties of Fuchsian groups, and also on probabilistic generation of groups of Lie type.
In these notes we will survey recent results on various finitary approximation properties of infinite groups. We will discuss various restrictions on groups that are approximated for example by finite solvable groups or finite-dimensional…
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…
Under certain conditions on k we calculate the limit distribution of the k:th largest eigenvalue, x_k, of the Gaussian Unitary Ensemble (GUE). More specifically, if n is the dimension of a random matrix from the GUE and k is such that both…
Expanding products of invariant functions of a group element as a series in the basis of characters of the irreducible representations of a group is widely used in many areas of physics and related fields. In this contribution a formula to…
We study multiplicities of unipotent characters in tensor products of unipotent characters of GL(n,q). We prove that these multiplicities are polynomials in q with non-negative integer coefficients. We study the degree of these polynomials…
We obtain a non--trivial upper bound for the multiplicative energy of any sufficiently large subset of a subvariety of a finite algebraic group. We also find some applications of our results to growth of conjugates classes, estimates of…
We find upper and lower bounds of the multiplicities of irreducible admissible representations $\pi$ of a semisimple Lie group $G$ occurring in the induced representations $Ind_H^G\tau$ from irreducible representations $\tau$ of a closed…
The number of points on a hyperelliptic curve over a field of $q$ elements may be expressed as $q+1+S$ where $S$ is a certain character sum. We study fluctuations of $S$ as the curve varies over a large family of hyperelliptic curves of…
We show that, for general convolution approximations to a large class of log-correlated Gaussian fields, the properly normalised supercritical Gaussian multiplicative chaos measures converge stably to a nontrivial limit. This limit depends…
We study systematically groups whose marked finite quotients form a recursive set. We give several definitions, and prove basic properties of this class of groups, and in particular emphasize the link between the growth of the depth…
We prove a factorization-concentration result for characters of symmetric groups. This is then applied to the asymptotic behaviour of the decomposition of the tensor representations. There are connections with the Pastur-Marcenko…
The q-characters of quantum loop algebras are very important objects in representation theory. In [20], we showed that q-characters factor as a power series of the form studied in [9] times a character, an important phenomenon which had…
We prove a broad generalization of a theorem of W. Burnside on real characters using permutation characters. Under a necessary hypothesis, We can give some control on multiplicities (a result that needs the Classification of Finite Simple…