Related papers: De Rham - Witt KZ equations

The sum formula for multiple zeta values are derived, via the Mellin transform, from the Euler connection formula and the Landen connection formula for polylogarithms. These connection formulas for multiple polylogarithms will be considered…

Let A be a finitely generated algebra over a field K of characteristic p >0. We introduce a subring of the ring of Witt vectors W(A). We call it the ring of overconvergent Witt vectors. We prove that on a scheme X of finite type over K the…

We describe the general strategy for lifting the Wess-Zumino-Witten model from the level of one-loop Kac-Moody $U_q(\widehat{\mathfrak{g}})_k$ to generic quantum toroidal algebras. A nearly exhaustive presentation is given for the two…

New recursion relations for the Riemann zeta function are introduced. Their derivation started from the standard functional equation. The new functional equations have both real and imaginary increment versions and can be applied over the…

Derived de Rham cohomology has been recently used in several contexts, as in works of Beilinson and Bhatt on p-adic periods morphisms and Morin on numerical invariants for special values of zeta functions. Inspired by some results of Morin,…

This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…

The trigonometric KZ equations associated to a Lie algebra \g depend on a parameter \lambda in \h where \h is a Cartan subalgebra of \g. A system of dynamical difference equations with respect to \lambda compatible with the KZ equations is…

We announce new methods for using prismatic cohomology to compute the K-groups of $\mathbb{Z}/p^n$ and related rings. We use computer algebra methods to compute these K-groups through a large range in specific cases and also obtain explicit…

The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal algebras. In this paper, we develop cohomology theory of Hom-Lie conformal algebras and…

We give the hypergeometric solutions of some algebraic equations including the general fifth degree equation.

We develop the theory of linear algebra over a (Z_2)^n-commutative algebra (n in N), which includes the well-known super linear algebra as a special case (n=1). Examples of such graded-commutative algebras are the Clifford algebras, in…

This thesis is devoted to the study of three problems on the Wess-Zumino-Witten (WZW) and Chern-Simons (CS) supergravity theories in the Hamiltonian framework: 1) The two-dimensional super WZW model coupled to supergravity is constructed.…

In this paper we construct irregular representations of the affine Kac-Moody algebra $\widehat{sl}(2,\mathbb{C})$. We show how such irregular representations correspond to irregular Gaiotto-Teschner representations of the Virasoro algebra.…

The aim of this paper is to give an alternative proof of Kac's theorem for weighted projective lines (\cite{W}) over the complex field. The geometric realization of complex Lie algebras arising from derived categories (\cite{XXZ}) is…

In this sequel to arxiv:arXiv:1012.0835 we develop Bezout type theorems for semidegrees (including an explicit formula for {\em iterated semidegrees}) and an inequality for subdegrees. In addition we prove (in case of surfaces) a Bernstein…

We construct confluent KZ equations with Poincare rank 2 at infinity for the case of sl_N and the integral representation for the solutions. Hamiltonians of these confluent KZ equations are derived from suitable quantization of dlog tau…

A simple formal recasting of well known arguments concerning the ordering problems of General Relativity allows to obtain in such a context a Gr\"{o}enewald Van Hove like theorem.

We study dynamics of the Latt\`es maps in the complex plane in terms of the Cuntz-Krieger algebras associated to the endomorphisms of the non-commutative tori. In particular, it is shown that iterations of the Latt\`es maps can be reduced…

We give a parametrization with perfect sets of the abstract Ellentuck theorem. The main tool for achieving this goal is a sort of parametrization of an abstract version of the Nash-Williams theorem. As corollaries, we obtain some known…

We consider the KZ differential equations over $\mathbb C$ in the case, when the hypergeometric solutions are one-dimensional integrals. We also consider the same differential equations over a finite field $\mathbb F_p$. We study the space…