Related papers: Stokes factors and multilogarithms

The classical problem of computing a complete system of Stokes multipliers of a linear system of ODEs of rank one in terms of some connection coefficients of an associated hypergeometric system of ODEs, is solved with no genericness…

We point out, and draw some consequences of, the fact that the Poisson Lie group G* dual to G=GL_n(C) (with its standard complex Poisson structure) may be identified with a certain moduli space of meromorphic connections on the unit disc…

Using a m\'elange of techniques at the rich intersection of deformation/rigidity theory, finite index subfactor theory, and geometric group theory, we prove the existence of a continuum of property (T) factors that are pairwise non-stably…

It is a consequence of the Jacobi Inversion Theorem that a line bundle over a Riemann surface M of genus g has a meromorphic section having at most g poles, or equivalently, the divisor class of a divisor D over M contains a divisor having…

The author presents the generalized Stokes theorem for R-linear forms on Lie algebroids (which can be non-local). We apply the Stokes formula on forms to prove that two homotopic homomorphisms of Lie algebroids implies the existence of a…

We show that any semi-direct sum $L$ of Lie algebras with Levi factor $S$ must be perfect if the representation associated with it does not possess a copy of the trivial representation. As a consequence, all invariant functions of $L$ must…

We generalize both the notion of polynomial functions on Lie groups and the notion of horizontally affine maps on Carnot groups. We fix a subset $S$ of the algebra $\mathfrak g$ of left-invariant vector fields on a Lie group $\mathbb G$ and…

We study the structure of the Lie algebra $\mathfrak{s}(n,\mathbb R)$ corresponding to the so-called stochastic Lie group $\mathcal{S} (n,\mathbb R)$. We obtain the Levi decomposition of the Lie algebra, classify Levi factor and classify…

We study finite-rank left-translation invariant algebraic $D$-modules on complex affine algebraic groups. Using the standard description of these objects as left-invariant flat algebraic connections on the trivial vector bundle, modulo…

We introduce the basic notions and present examples and results on Lie categories -- categories internal to the category of smooth manifolds. Demonstrating how the units of a Lie category $\mathcal C$ dictate the behavior of its invertible…

Let k be a perfect field and A a finite dimensional k-algebra of finite global dimension (e.g. the path algebra of a finite quiver without oriented cycles). Making use of the recent theory of noncommutative motives, we prove that the value…

We consider the 2-generated free metabelian associative and Lie algebras over the complex field and the invariants of the dihedral groups of finite order acting on these algebras. In the associative case we find a finite set of generators…

Let V be a finite dimensional complex superspace and G a simple (or a ``close'' to simple) Lie superalgebra of matrix type, i.e., a Lie subsuperalgebra in GL(V). Under the classical invariant theory for G we mean the description of…

For an adjoint action of a Lie group G (or its subgroup) on Lie algebra Lie(G) we suggest a method for construction of invariants. The method is easy in implementation and may shed the light on algebraical independence of invariants. The…

We prove that there are infinitely many finite simple groups of symplectic Lie type, of any specified characteristic and rank, which appear as Galois groups over the field of rational numbers. This generalizes a result of Wiese, which…

We determine the composition factors of the tensor product $S(E)\otimes S(E)$ of two copies of the symmetric algebra of the natural module $E$ of a general linear group over an algebraically closed field of positive characteristic. Our main…

We prove an analogue of Lowrey--Sch\"urg's algebraic Spivak's theorem when working over a base ring $A$ that is either a field or a nice enough discrete valuation ring, and after inverting the residual characteristic exponent $e$ in the…

This is the second paper in a series on intrinsic Donaldson-Thomas theory, a framework for studying the enumerative geometry of general algebraic stacks. In this paper, we present the construction of Donaldson-Thomas invariants for general…

This paper is a continuation of our previous work \cite{St} where we have studied the Stokes phenomenon for a particular family of equation \eqref{initial} with \eqref{form-0}-\eqref{npe} from a perturbative point of view. Here we focus on…

Many versions of the Stokes theorem are known. More advanced of them require complicated mathematical machinery to be formulated which discourages the users. Our theorem is sufficiently simple to suit the handbooks and yet it is pretty…