Related papers: AGC, t-designs and partition sets

Using a general result of Lusztig, we give explicit formulas for the dimensions of K^F-invariants in irreducible representations of G^F, when G=GL_n, F:G->G is a Frobenius map, and K is an F-stable subgroup of finite index in G^theta for…

Let F<X> be the free unitary associative algebra over a field F on the set X = {x_1, x_2, ...}. A vector subspace V of F<X> is called a T-subspace (or a T-space) if V is closed under all endomorphisms of F<X>. A T-subspace V in F<X> is…

The algebraic formulation of the quantum group covariant noncommutative geometry in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider structure groups taking values in the quantum groups and…

A characterization of finitely generated shift-invariant subspaces is given when generators are g-minimal. An algorithm is given for the determination of the coefficients in the well known representation of the Fourier transform of an…

The Shape invariant method has the algebraic structure and its algebras are infinite-dimensional. These algebras are converted into finite-dimensional under conditions. Based on the property of this method we obtain the algebraic structure…

We give a proof of a result of D. Peterson's identifying the quantum cohomology ring of a Grassmannian with the reduced coordinate ring of a certain subvariety of $GL_n$. The totally positive part of this subvariety is then constructed and…

A $k$-polar Grassmannian is the geometry having as pointset the set of all $k$-dimensional subspaces of a vector space $V$ which are totally isotropic for a given non-degenerate bilinear form $\mu$ defined on $V.$ Hence it can be regarded…

A $2$-$(v,k,\lambda)$ design is additive (or strongly additive) if it is possible to embed it in a suitable abelian group $G$ in such a way that its block set is contained in (or coincides with) the set of all the zero-sum $k$-subsets of…

The aim of this paper is to present a construction of $t$-divisible designs for $t>3$, because such divisible designs seem to be missing in the literature. To this end, tools such as finite projective spaces and their algebraic varieties…

In this note we consider representations of the group GL(n,F), where F is the field of real or complex numbers or, more generally, an arbitrary local field, in the space of equivariant line bundles over Grassmannians over the same field F.…

Discussed are field-theoretic models with degrees of freedom described by the $n$-leg field in an $n$-dimensional "space-time" manifold. Lagrangians are generally-covariant and invariant under the internal group GL$(n,{\bf R})$. It is shown…

In this paper we investigate multi-point Algebraic-Geometric codes associated to the GK maximal curve, starting from a divisor which is invariant under a large automorphism group of the curve. We construct families of codes with large…

In this paper, we construct a combinatorial algebra of partial isomorphisms that gives rise to a "projective limit" of the centers of the group algebras C[GL(n,Fq)]. It allows us to prove a GL(n,Fq)-analogue of an old theorem of Farahat and…

When $G$ is a complex reductive algebraic group and $G/K$ is a reductive symmetric space, the decomposition of $\C[G/K]$ as a $K$-module was obtained (in a non-constructive way) by Richardson, generalizing the celebrated result of…

Consider the Grassmann graph of $k$-dimensional subspaces of an $n$-dimensional vector space over the $q$-element field, $1<k<n-1$. Every automorphism of this graph is induced by a semilinear automorphism of the corresponding vector space…

Consider a finite triangulation of a surface $M$ of genus $g$ and assume that spin-less fermions populate the edges of the triangulation. The quantum dynamics of such particles takes place inside the algebra of canonical anti-commutation…

We point out an explicit connection between graphs drawn on compact Riemann surfaces defined over the field $\bar{\mathbb{Q}}$ of algebraic numbers --- so-called Grothendieck's {\it dessins d'enfants} --- and a wealth of distinguished…

We study the specializations $\mathcal{L}_{g,n}^\epsilon$ at roots of unity $\epsilon$ of odd order of the graph algebras, associated to a simply-connected complex semi-simple algebraic group $G$ and a compact oriented surface…

We prove finite generation of the algebras of invariants for a class of linear actions of suitable non-reductive groups on projective and affine varieties, and give a geometric construction for their GIT quotients.

It was shown in \cite{FPV} that the classification of $n$-component systems of conservation laws possessing a third-order Hamiltonian structure reduces to the following algebraic problem: classify $n$-planes $H$ in $\wedge^2(V_{n+2})$ such…