Related papers: First and Second Fundamental Theorems for Invarian…

Let $R_1$ be a commutative ring, let $R_2$ be a finitely generated extension ring of $R_1$, and let $S$ be a ring that is intermediate between $R_1$ and $R_2$. For $R_1 = R[x]$ and $R_2 = R[x,y]$, this paper gives simple combinatorial…

We focus on working on incidence rings, a class of (possibly infinite) matrix rings indexed by ordered sets. Some general properties about them are given, including how they are always the inverse limit of finite matrix rings, giving a…

The work proves that, for three-dimensional upper triangular groups over a field of odd characteristic with an abelian unipotent subgroup, the ring of invariants is polynomial if and only if the unipotent subgroup is generated by…

The invariant theory of finite groups can connect the coding theory to the number theory. In this paper, under this conformity, we obtain the minimal generators of the rings of E-polynomials constructed from the groups related to…

We identify a number of decidable and undecidable fragments of first-order concatenation theory. We also give a purely universal axiomatization which is complete for the fragments we identify. Furthermore, we prove some normal-form results.

The main result of this paper is a generalization of the theorem of Chevalley-Shephard-Todd to the rings of invariants of pseudo-reflection groups over regular domains. More precisely, let $A$ be a regular domain and let $K$ be its field of…

It is shown that a trivial version of polarization is sufficient to produce separating systems of polynomial invariants: if two points in the direct sum of the $G$--modules $W$ and $m$ copies of $V$ can be separated by polynomial…

For ring of differential operators on smooth affine algebraic variety over perfect field of prime characteristic a set of algebra generators and a set of defining relations are found explicitly.

In this paper, we study the vector invariants, ${\bf{F}}[m V_2]^{C_p}$, of the 2-dimensional indecomposable representation $V_2$ of the cylic group, $C_p$, of order $p$ over a field ${\bf{F}}$ of characteristic $p$. This ring of invariants…

Let $X$ be a nonempty real variety that is invariant under the action of a reflection group $G$. We conjecture that if $X$ is defined in terms of the first $k$ basic invariants of $G$ (ordered by degree), then $X$ meets a $k$-dimensional…

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 present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…

We prove a nonconventional invariance principle (functional central limit theorem) for random fields.

First order lagrangians for the Weyl invariant formulation of Unimodular Gravity are proposed. Several alternatives are examined; in some of them first and second order are equivalent in a certain gauge only.

The possibility of variations of the values of fundamental constants is a phenomenon predicted by a number of scenarios beyond General Relativity. This can happen if ``our'' fundamental constants are not the actual constants of the…

An underlying fundamental assumption in relativistic perturbation theory is the existence of a parametric family of spacetimes that can be Taylor expanded around a background. Since the choice of the latter is crucial, sometimes it is…

For modular indecomposable representations of a cyclic group $G$ of prime order $p$ we propose a list of polynomial invariants of degree $\leq 3$ that, together with a simple invariant of degree $p$, separate generic orbits and generate the…

This work presents closed formulas for determinant, permanent, inverse, and Drazin inverse of circulant matrices with two non-zero coefficients.

This thesis addresses questions in representation and invariant theory of finite groups. The first concerns singularities of quotient spaces under actions of finite groups. We introduce a class of finite groups such that the quotients have…

It has been known that there exists a canonical system for every finite real reflection group. The first and the third authors obtained an explicit formula for a canonical system in the previous paper. In this article, we first define…