Related papers: Stabilizer group of generalized determinant
We give an introduction to some of the recent ideas that go under the name "geometric complexity theory". We first sketch the proof of the known upper and lower bounds for the determinantal complexity of the permanent. We then introduce the…
Let $G$ be a permutation group on the finite set $\Omega$. We prove various results about partitions of $\Omega$ whose stabilizers have good properties. In particular, in every solvable permutation group there is a set-stabilizer whose…
We determine which faithful irreducible representations $V$ of a simple linear algebraic group $G$ are generically free for Lie($G$), i.e., which $V$ have an open subset consisting of vectors whose stabilizer in Lie($G$) is zero. This…
Another stabilizer term is used in the classical Hamiltonian of the Skyrme Model that permits in a much simple way the generalization of the higher-order terms in the pion derivative field. Improved numerical results are obtained.
We describe a situation where an unstable equilibrium in a $3 \times 3$ system of linear differential equations may be stabilized by introducing a delayed response, i.e. converting to a system of delayed differential equations. This…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…
We consider an arbitrary representation of the additive group over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants.
In this short note we formulate a stabilizer formalism in the language of noncommutative graphs. The classes of noncommutative graphs we consider are obtained via unitary representations of compact groups, and suitably chosen operators on…
A group pair $(G, X)$ consists of a group $G$ together with a $G$-set $X$. Such a pair encodes properties of $G$ relative to the stabilisers of points in $X$. In this paper, we show how to combine properties of group pairs and their…
A 2-dimensional point-line framework is a collection of points and lines in the plane which are linked by pairwise constraints that fix some angles between pairs of lines and also some point-line and point-point distances. It is rigid if…
Linear-constraint loops are programs whose transition relation is specified by a system of linear inequalities. The termination problem asks, given a loop, whether it admits an infinite computation. Decidability of termination remains open…
We investigate compositions of a positive integer with a fixed number of parts, when there are several types of each natural number. These compositions produce new relationships among binomial coefficients, Catalan numbers, and numbers of…
We investigate the structure of the centralizer and the normalizer of a local analytic or formal differential system at a nondegenerate stationary point, using the theory of Poincar\'e-Dulac normal forms. Our main results are concerned with…
A VI-module gives rise to a sequence of representations of the finite general linear groups. We prove that the sequence obtained from any finitely generated VI-module over an algebraically closed field of characteristic zero is…
This is a survey of results about permanental processes, real valued positive processes which are a generalization of squares of Gaussian processes. In a certain sense the symmetric positive definite function that determines a Gaussian…
This paper focuses on the stabilization and regulation of linear systems affected by quantization in state-transition data and actuated input. The observed data are composed of tuples of current state, input, and the next state's interval…
This paper investigates the toral stabilizer of a finite-dimensional restricted Lie algebra $(\mathfrak{g},[p])$, defined over an algebraically closed field $k$ of positive characteristic. We compute the group of toral stabilizers of some…
Consider a nonsolvable finite group G, where R(G) represents the solvable radical of G. For any element x in G, the solvabilizer of x in G, denoted by Sol_G(x), is defined as the set of all elements y in G such that the subgroup generated…
This paper studies a partial order on the general linear group GL(V) called the absolute order, derived from viewing GL(V) as a group generated by reflections, that is, elements whose fixed space has codimension one. The absolute order on…
We study a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized…