Related papers: Arithmetic infinite Grassmannians and the induced …
The $H$-ring structure of certain infinite(-dimensional) Grassmannians is discussed using various algebraic and analytical methods but so that cellular arguments are avoided. These methods allow us to discuss these Grassmannian in greater…
We describe the T-space of central polynomials for both the unitary and the nonunitary infinite dimensional Grassmann algebra over a field of characteristic p not equal to 2 (infinite field in the case of the unitary algebra).
We associate with a matrix over an arbitrary field an infinite family of matrices whose sizes vary from one to infinity; their entries are traces of powers of the original matrix. We explicitly evaluate the determinants of matrices in our…
This paper aims at generalizing some geometric properties of Grassmannians of finite dimensional vector spaces to the case of Grassmannnians of infinite dimensional ones, in particular for that of $k((z))$. It is shown that the Determinant…
The aim of this paper is to offer an algebraic construction of infinite-dimensional Grassmannians and determinant bundles (and therefore valid for arbitrary base fields). As an application we construct the $\tau$-function and formal…
An algebraic approach is developed to define and study infinite dimensional grassmannians. Using this approach a quantum deformation is obtained for both the ind-variety union of all finite dimensional grassmannians, and the Sato…
An infinite family of nonschurian separable association schemes is constructed.
We describe the T-ideal of identities and the T-space of central polynomials for the infinite dimensional unitary Grassmann algebra over a finite field.
We describe the T-space of central polynomials for both the unitary and the nonunitary finite dimensional Grassmann algebra over a field of characteristic p not equal to 2 (infinite field in the case of the unitary algebra).
The main result of this paper is the explicit computation of the equations defining the moduli space of triples $(C,p,z)$ (where $C$ is an integral and complete algebraic curve, $p$ a smooth rational point and $z$ a formal trivialization…
We compute the elementary divisors of the adjacency and Laplacian matrices of the Grassmann graph on $2$-dimensional subspaces in a finite vector space. We also compute the corresponding invariants of the complementary graphs.
In this paper we consider Grassmannians in arbitrary characteristic. Generalizing Kapranov's well-known characteristic-zero results we construct dual exceptional collections on them (which are however not strong) as well as a tilting…
We will pursue a way of building up an algebraic structure that involves, in a mathematical abstract way, the well known Grassmann variables. The problem arises when we tried to understand the grassmannian polynomial expansion on the scope…
We present several principal bundles of embeddings of compact manifolds (with or without boundary) whose base manifolds are nonlinear Grassmannians. We study their infinite dimensional differential manifold structure in the Fr\'echet…
Formulations of some Grassmann-valued systems of ordinary differential equations invariant under (infinitesimal) supersymmetry transformations, including $N$-superspace extended types, are reviewed and discussed, with use of superfields.…
The regular point-line geometry with respect to a pseudo-polarity is introduced. It is weaker than the underlying metric-projective geometry. The automorphism group of this geometry is determined. This geometry can be also expressed as the…
Let G be a simple simply-connected group scheme over a regular local scheme U. Let E be a principal G-bundle over A^1_U trivial away from a subscheme finite over U. We show that E is not necessarily trivial and give some criteria of…
We give an explicit description of the category of central extensions of a group scheme by a sheaf of Abelian groups. Based on this, we describe a framework for computing with central extensions of finite commutative group schemes, torsors…
Every finite flat finitely presented group scheme G of square free order over a scheme S can be written as an extension of a finite etale S-group scheme G" by a commutative finite flat finitely presented S-group scheme G' that is a direct…
We first prove an identity involving symmetric polynomials. This identity leads us into exploring the geometry of Lagrangian Grassmannians. As an insight applications, we obtain a formula for the integral over the Lagrangian Grassmannian of…