Related papers: On computing joint invariants of vector fields
We define a new invariant for a $p$-block, the strong Frobenius number, which we use to address the problem of reducing Donovan's conjecture to normal subgroups of index p. As an application we use the strong Frobenius number to complete…
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…
We first prove a Cauchy's integral theorem and Cauchy type formula for certain inhomogeneous Cimmino system from quaternionic analysis perspective. The second part of the paper directs the attention towards some applications of the…
We determine the probability, structure dependent, that the block Wiedemann algorithm correctly computes leading invariant factors. This leads to a tight lower bound for the probability, structure independent. We show, using block size…
In this paper, we define a set of good basic invariants for a finite complex reflection group under certain conditions. We show that a set of good basic invariants for a finite real reflection group gives a set of the flat invariants…
We prove some injectivity theorems. Our proof depends on the theory of mixed Hodge structures on cohomology groups with compact support. Our injectivity theorems would play crucial roles in the minimal model theory for higher-dimensional…
The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.
We reformulate the theory of p-adic iterated integrals on semistable curves using the unipotent log rigid fundamental group. This fundamental group carries Frobenius and monodromy operators whose basic properties are established. By…
In the past few years, an action of $\mathrm{PGL}_2(\mathbb F_q)$ on the set of irreducible polynomials in $\mathbb F_q[x]$ has been introduced and many questions have been discussed, such as the characterization and number of invariant…
We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. Applying our methods to several field theories such as abelian BF, Chern-Simons and 2-dimensional…
The goal of this note is to exhibit the integrability properties (in the sense of the Frobenius theorem) of holomorphic p-forms with values in certain line bundles with seminegative curvature on a compact Kaehler manifold. There are in fact…
In this short review we first recall combinatorial or ($0-$dimensional) quantum field theory (QFT). We then give the main idea of a standard QFT method, called the intermediate field method, and we review how to apply this method to a…
I adapt a recently introduced method for integrating over the unitary group (S. Aubert and C.S. Lam, J.Math.Phys. 44, 6112-6131 (2003)) to the orthogonal group. I derive explicit formulas for a number of one, two and three-vector integrals,…
In this paper we present an equivalent statement to the Jacobian conjecture. For a polynomial map F on an affine space of dimension n, we define recursively n finite sequences of polynomials. We give an equivalent condition to the…
The functional integral computation of the various topological invariants, which are associated with the Chern-Simons field theory, is considered. The standard perturbative setting in quantum field theory is rewieved and new developments in…
We introduce a weighted sum of irreducible character ratios as an estimator for commutator probabilities. The estimator yields Frobenius formula when applied to a regular representation
Higher genus partition functions of two-dimensional conformal field theories have to be invariants under linear actions of mapping class groups. We illustrate recent results [4,6] on the construction of such invariants by concrete…
Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…
We present a new structure theorem for finite fields of odd order that relates multiplicative and additive structure in an interesting way. This theorem has several applications, including an improved understanding of Dickson and Chebyshev…
We study unitary representations of groups in Krein spaces, irreducibility criteria and integral decompositions. Our main tool is the theory of Krein subspaces and their (reproducing) kernels and a variant of Choquet's theorem.