Related papers: Character expansion of matrix integrals
A new family of asymmetric matrices of Walsh-Hadamard type is introduced. We study their properties and, in particular, compute their determinants and discuss their eigenvalues. The invertibility of these matrices implies that certain…
For one-matrix models with polynomial potentials, the explicit relationship between the partition function and the isomonodromic tau function for the 2x2 polynomial differential systems satisfied by the associated orthogonal polynomials is…
In 2015, the author proved combinatorially character formulas expressing sums of the (formal) dimensions of irreducible representations of symplectic groups, refining some works of Nekrasov and Okounkov, Han, King, and Westbury. In this…
For any arbitrary algebraic curve, we define an infinite sequence of invariants. We study their properties, in particular their variation under a variation of the curve, and their modular properties. We also study their limits when the…
Motivated by a model in quantum computation we study orthogonal sets of integral vectors of the same norm that can be extended with new vectors keeping the norm and the orthogonality. Our approach involves some arithmetic properties of the…
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 present a genus expansion-type expression for the expected values of products of traces of expressions involving Haar-distributed orthogonal matrices. As with other real genus expansions, nonorientable surfaces appear, in addition to the…
We generalise Gelfand-Graev characters to $\mathbb R/\mathbb Z$-graded Lie algebras and lift them to produce new test functions to probe the local character expansion in positive depth. We show that these test functions are well adapted to…
: Algebraic properties of orbifold models on arbitrary Riemann surfaces are investigated. The action of mapping class group transformations and of standard geometric operations is given explicitly. An infinite dimensional extension of the…
We introduce self-similar algebras and groups closely related to the Thue-Morse sequence, and begin their investigation by describing a character on them, the "spread" character.
The skew Schur functions admit many determinantal expressions. Chief among them are the (dual) Jacobi-Trudi formula and the Lascoux-Pragacz formula, which is a skew analogue of the Giambelli identity. Comparatively, the skew characters of…
We consider a class of functions for which the multiple Stratonovich stochastic integral or equivalent iterated Stratonovich stochastic integral with square integrable weights is defined by the orthogonal expansion. The equality of the…
Let $x \in [0,1)$ be a real number and denote its continued fraction expansion by $[a_1(x),a_2(x), a_3(x),\cdots]$. The convergence exponent of these partial quotients is defined as \[ \tau(x):= \inf\left\{s \geq 0: \sum_{n \geq 1}…
Let V be a symplectic vector space over a finite or local field. We compute the character of the Weil representation of the metaplectic group Mp(V). The final formulas are overtly free of choices (e.g. they do not involve the usual choice…
In view of applications to conformal field theory or to other branches of theoretical physics and mathematics, new examples of character tables for Drinfeld doubles of finite groups (modular data) are made available on a website.
The paper presents a classification of quadratic extension algebras, also known as algebras of degree 2, as well as several characterizations of quaternion algebras over a field (of characteristic not 2). The presentation is not restricted…
A new series expansion for the function (arctan(x)/x)^n is developed and some properties of the expansion coefficients are obtained.
We continue the study of character sheaves on a not necessarily connected reductive group. We prove orthogonality formulas for certain characteristic functions.
We characterize asymptotic collective behaviour of rectangular random matrices, the sizes of which tend to infinity at different rates: when embedded in a space of larger square matrices, independent rectangular random matrices are…
A characterization of multiplicative (and additive) arithmetical functions is given. Using this characterization, we show that the group of multiplicative arithmetical functions is isomorphic to the group of additive arithmetical functions.