Related papers: The stabilizer of a column in a matrix group over …

We develop a new renormalization group approach to the large-N limit of matrix models. It has been proposed that a procedure, in which a matrix model of size (N-1) \times (N-1) is obtained by integrating out one row and column of an N…

Let $D_n$ be the dihedral group with $2n$ elements, and suppose $n$ is greater than one. We call ring system a finite $D_n$-symmetric set of points in $\mathbb{R}^2$. Ring systems have been used as models for planets surrounded by rings,…

This is the second of two papers treating faithful actions of simple algebraic groups on irreducible modules and on the associated Grassmannian varieties; in the first paper we considered the module itself and its projective space, while…

We consider rational projective homogeneous varieties over an algebraically closed field of positive characteristic, namely quotients of a semi-simple group by a possibly non-reduced parabolic subgroup. We determine the group scheme…

Let $R$ be a (not necessarily commutative) ring whose additive group is finitely generated and let $U_n(R) \subset GL_n(R)$ be the group of upper-triangular unipotent matrices over $R$. We study how the homology groups of $U_n(R)$ vary with…

We study subgroups $H_U$ of the R. Thompson group $F$ which are stabilizers of finite sets $U$ of numbers in the interval $(0,1)$. We describe the algebraic structure of $H_U$ and prove that the stabilizer $H_U$ is finitely generated if and…

In casual discussion, a stack is often described as a variety (the coarse space) together with stabilizer groups attached to some of its subvarieties. However, this description does not uniquely specify the stack. Our main result shows that…

The description of the automorphism group of group $<a, b; [a^m,b^n]=1>$ ($m,n>1$) in terms of generators and defining relations is given. This result is applied to prove that any normal automorphism of every such group is inner.

To a set $\mathcal{B}$ of 4-subsets of a set $\Omega$ of size $n$ we introduce an invariant called the `hole stabilizer' which generalises a construction of Conway, Elkies and Martin of the Mathieu group $M_{12}$ based on Loyd's…

We study the problem of determining, for a polynomial function $f$ on a vector space $V$, the linear transformations $g$ of $V$ such that $f g = f$. In case $f$ is invariant under a simple algebraic group $G$ acting irreducibly on $V$, we…

We study the polynomial algebra (over a ring containing the rationals) in an n by m matrix of variables, and subject to the relation that says that the product of any two variables in the same column is zero. We show that the sub-algebra of…

We show that static data structure lower bounds in the group (linear) model imply semi-explicit lower bounds on matrix rigidity. In particular, we prove that an explicit lower bound of $t \geq \omega(\log^2 n)$ on the cell-probe complexity…

This article began as a study of the structure of infinite permutation groups G in which point stabilisers are finite and all infinite normal subgroups are transitive. That led to two variations. One is the generalisation in which point…

For a positive integer $n\geq 3$, the sides and diagonals of a convex $n$-gon divide the interior of the convex $n$-gon into finitely (polynomial in $n$) many regions bounded by them. In this article, we associate to every region a unique…

We prove a general homological stability theorem for certain families of groups equipped with product maps, followed by two theorems of a new kind that give information about the last two homology groups outside the stable range. (These…

Let $H$ be a group and $E$ a set such that $H \subseteq E$. We shall describe and classify up to an isomorphism of groups that stabilizes $H$ the set of all group structures that can be defined on $E$ such that $H$ is a subgroup of $E$. A…

We prove a myriad of results related to the stabilizer in an algebraic group $G$ of a generic vector in a representation $V$ of $G$ over an algebraically closed field $k$. Our results are on the level of group schemes, which carries more…

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…

In this paper we analyze the structure of transitive permutation groups that have trivial four point stabilizers, but some nontrivial three point stabilizer. In particular we give a complete, detailed classification when the group is simple…

This manuscript represents the author's PhD dissertation thesis.The first part studies decision problems in Thompson's groups F,T,V and some generalizations. The simultaneous conjugacy problem is determined to be solvable for Thompson's…