Related papers: On reducible monodromy representations of some gen…

The group classification problem for the class of (1+1)-dimensional linear $r$th order evolution equations is solved for arbitrary values of $r>2$. It is shown that a related maximally gauged class of homogeneous linear evolution equations…

We compute the module of universal norms for a de Rham p-adic representation. The computation uses the theory of (phi,Gamma)-modules (Cherbonnier-Colmez's reciprocity formula) and the differential equation attached to a de Rham…

The aim of this paper is to present an explicit reduction algorithm for Hilbert modular groups over arbitrary totally real number fields. An implementation of the algorithm is available to download from [19]. The exposition is…

Multiple actions of the monodromy matrix elements onto off-shell Bethe vectors in the $\mathfrak{gl}(m|n)$-invariant quantum integrable models are calculated. These actions are used to describe recursions for the highest coefficients in the…

Several problems in number theory when reformulated in terms of homogenous dynamics involve study of limiting distributions of translates of algebraically defined measures on orbits of reductive groups. The general non-divergence and…

This paper is devoted to Riemann-Hilbert problems with constraints. We obtain results characterizing the existence of solutions as well as the dimension of the solution space in terms of certain indices. As an application, we show how such…

For the isotropic Lam\'e system, we prove in dimensions three or larger that both Lam\'e coefficients are uniquely recovered from partial Cauchy data on an arbitrary open subset of the boundary provided that the coefficient $\mu$ is a…

For a semisimple, simply-connected linear algebraic group, $G$, and parabolic subgroup, $P\subseteq G$, we use the fact that the Hilbert polynomial of the equivariant embedding of $G/P$ is equal to the Hilbert function to compute an…

We give an algorithm for computing the irreducible admissible representations of a real reductive group with regular integral infinitesimal character. This algorithm has been implemented on a computer, as part of the Atlas of Lie Groups and…

The planar Kepler problem is complexified and we show that this holomorphic completely integrable Hamiltonian system has nontrivial monodromy.

We propose a systematic method for analyzing Rohrlich-type divisor sums for arbitrary congruence subgroups $\Gamma_0(N)$. Our main theorem unifies various results from the literature, and its significance is illustrated through the…

A recently proposed integral representation for permanents is rederived using only elementary combinatorics. For this proof the assumption that the matrix, for which the permanent is calculated, has an inverse is not necessary.

In one complex variable, the existence of a compactly supported solution to the Cauchy-Riemann equation is related to the vanishing of certain integrals of the data; trying to generalize this approach, we find an explicit construction, via…

For any branched double covering of compact Riemann surfaces, we consider the associated character varieties that are unitary in the global sense, which we call $\text{GL}_n\rtimes\!<\!\sigma\!>\!~$-character varieties. We restrict the…

Recently found all the fundamental solutions of a multidimensional singular elliptic equation are expressed in terms of the well-known Lauricella hypergeometric function in many variables. In this paper, we find a unique solution of the…

Repeated integration is a major topic of integral calculus. In this article, we study repeated integration. In particular, we study repeated integrals and recurrent integrals. For each of these integrals, we develop reduction formulae for…

Employing a suitable nonlinear Lagrange functional, we derive generalized Hamilton-Jacobi equations for dynamical systems subject to linear velocity constraints. As long as a solution of the generalized Hamilton-Jacobi equation exists, the…

The main purpose of this paper is providing a simple method to generate the matrices of irreducible representations because it is useful to reduce the computational time of solving the eigenvalue problems. The only information we need to…

We obtain a parametric normal form for any non-degenerate perturbation of the generalized saddle-node case of Bogdanov--Takens singularity. Explicit formulas are derived and greatly simplified for an efficient implementation in any computer…

We give some additions to the article "On the generalized Riemann-Hilbert problem with irregular singularities" by Bolibruch, Malek, Mitschi (math/0410483). In particular, a weak GRH-problem and the GRH-problem for scalar differential…