Related papers: Wick rotation for D-modules

In this article we are examining extensions and some basic diagrammatic properties of modules, in both cases from a new, "virtual" point of view. As natural background for investigating the kind of problems we are dealing with, the virtual…

For a linear Dirac field on a globally hyperbolic static space-time the analytic continuation of its Wightman functions (Green functions) to Schwinger functions and back at zero and finite temperature is shown.

Motivated by the cubic forms and anomaly cancellation formulas of Witten-Freed-Hopkins, we give some new cubic forms on spin, spin$^c$, spin$^{w_2}$ and orientable 12-manifolds respectively. We relate them to $\eta$-invariants when the…

The winding of a closed oriented geodesic around the cusp of the modular orbifold is computed by the Rademacher symbol, a classical function from the theory of modular forms. In this article, we introduce a new construction of winding…

We introduce deformations of the space of (multi-diagonal) harmonic polynomials for any finite complex reflection group of the form W=G(m,p,n), and give supporting evidence that this space seems to always be isomorphic, as a graded…

A Dwork family is a one-parameter monomial deformation of a Fermat hypersurface. In this paper we compute algebraically the invariant part of its Gauss-Manin cohomology under the action of certain subgroup of automorphisms. To achieve that…

The theory of operads (May, cyclic, modular, PROPs, etc) is extended to include higher dimensional phenomena, i.e. operations between operations, mimicking the algebraic structure on varieties of arbitrary dimensions, having marked…

We give an overview of the theory of $\wideparen{\mathcal{D}}$-modules on rigid analytic spaces and its applications to admissible locally analytic representations of $p$-adic Lie groups.

As is well-known, the Witten deformation of the De Rham complex computes the De Rham cohomology. In this paper we study the Witten deformation on a noncompact manifold and restrict it to differential forms which behave polynomially near…

An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.

Let (X,D) be a D-scheme in the sense of Beilinson and Bernstein, given by an algebraic variety X and a morphism O_X -> D of sheaves of rings on X. We consider noncommutative deformations of quasi-coherent sheaves of left D-modules on X, and…

In [5], Connes and Chamseddine defined a cycle in the general framework of noncommutative geometry. They computed this cycle for the Dirac operator on 4-dimensioanl manifolds. We propose a way to study the Connes-Chamseddine cycle from the…

For an embedding of sufficiently high degree of a smooth projective variety X into projective space, we use residues to define a filtered holonomic D-module (M, F) on the dual projective space. This gives a concrete description of the…

Let $R$ be a ring with unity, $\sigma$ an endomorphism of $R$ and $M_R$ a right $R$-module. In this paper, we continue studding $\sigma$-rigid modules that were introduced by Gunner et al. \cite{generalized/rigid}. We give some results on…

We introduce the notion of generalized Weyl modules for twisted current algebras. We study their representation-theoretic and combinatorial properties and connection to the theory of nonsymmetric Macdonald polynomials. As an application we…

We consider moduli spaces of dynamical systems of correspondences over the projective line as a generalization of moduli spaces of dynamical systems of endomorphisms on the projective line. We obtain the rationality of the moduli spaces.…

Let X be the group of weights of a maximal torus of a simply connected semisimple group over C and let W be the Weyl group. The semidirect product W(Q\otimes X/X) is called the extended Weyl group. There is a natural C(v)-algebra H called…

Integral geometry deals with those integral transforms which associate to ``functions'' on a manifold their integrals along submanifolds parameterized by another manifold. Basic problems in this context are range characterization--where…

Some features of extended loops are considered. In particular, the behaviour under diffeomorphism transformations of the wavefunctions with support on the extended loop space are studied. The basis of a method to obtain analytical…

We study D-modules and related invariants on the space of 2 x 2 x n hypermatrices for n >= 3, which has finitely many orbits under the action of G = GL_2 x GL_2 x GL_n. We describe the category of coherent G-equivariant D-modules as the…