Related papers: Reflexponents

We study multiplicative Diophantine approximation property of vectors and compute Diophantine exponents of hyperplanes via dynamics.

Let $G$ be a simple algebraic group over an algebraically closed field $k$ of characteristic $p$. The classification of the conjugacy classes of unipotent elements of $G(k)$ and nilpotent orbits of $G$ on $\operatorname{Lie}(G)$ is…

Covariant or invariant functions under a compact linear group can be expressed in terms of functions defined in the orbit space of the group. The semialgebraic relations defining the orbit spaces of all finite coregular real linear groups…

An integral representation for form-factors of exponential fields in the sine-Gordon model is proposed.

We define, via Gorenstein homomorphisms, a class of local rings over which there exist non-trivial totally reflexive modules. We also provide a general construction of such rings, which indicates their abundance.

The goal of invariant theory is to find all the generators for the algebra of representations of a group that leave the group invariant. Such generators will be called \emph{basic invariants}. In particular, we set out to find the set of…

The content of this preprint together with additional material appears now in 0706.2154.

Computation of spin-resummed observables in post-Minkowskian dynamics typically involve evaluation of Feynman integrals deformed by an exponential factor, where the exponent is a linear sum of the momenta being integrated. Such integrals…

We construct two combinatorially equivalent line arrangements in the complex projective plane such that the fundamental groups of their complements are not isomorphic. The proof uses a new invariant of the fundamental group of the…

We outline an algorithm for construction of functional bases of absolute invariants under the rotation group for sets of rank 2 tensors and vectors in the Euclidean space of arbitrary dimension. We will use our earlier results for symmetric…

We classify one-element extensions of a hyperplane arrangement by the induced adjoint arrangement. Based on the classification, several kinds of combinatorial invariants including Whitney polynomials, characteristic polynomials, Whitney…

Motivated by the classical ideas of generating functions for orthogonal polynomials, we initiate a new line of investigation on "generating operators" for a family of differential operators between two manifolds. We prove a novel formula of…

We construct highly singular projective curves and surfaces defined by invariants of primitive complex reflection groups.

We extend the theory of distributional kernel operators to a framework of generalized functions, in which they are replaced by integral kernel operators. Moreover, in contrast to the distributional case, we show that these generalized…

We introduce geometric invariants for $p$-groups of class $2$ and exponent $p$. We report on their effectiveness in distinguishing among 5-generator $p$-groups of this type.

For each subgroup of GL_2(F_p) or order divisible by p, generated by (pseudo-)reflections, we compute the ideals of stable and generalized invariants. These groups and these ideals are related to the cohomology of compact Lie groups,…

Optics, aka functional references, are classes of tools that allow composable access into compound data structures. Usually defined as programming language libraries, they provide combinators to manipulate different shapes of data such as…

This paper presents a new method for automatically generating numerical invariants for imperative programs. Given a program, our procedure computes a binary input/output relation on program states which over-approximates the behaviour of…

We study normal reflection subgroups of complex reflection groups. Our approach leads to a refinement of a theorem of Orlik and Solomon to the effect that the generating function for fixed-space dimension over a reflection group is a…

Sequences are often conveniently encoded in the form of a generating function depending on a formal variable. This note presents two observations that allow one to draw conclusions about the generated sequence from the generating function.…