Related papers: Arithmetic infinite Grassmannians and the induced …
We introduce a new infinite family of regular graphs admitting nested solutions in the edge-isoperimetric problem for all their Cartesian powers. The obtained results include as special cases most of previously known results in this area.
We provide a thorough construction of a system of compatible determinant line bundles over spaces of Fredholm operators, fully verify that this system satisfies a number of important properties, and include explicit formulas for all…
This paper generalizes the results of the paper \cite{mi3} to the case of the general $\mathfrak{sl}_2$ Schubert varieties. We study the homomorphisms between different Schubert varieties, describe their geometry and the group of the line…
We construct affine spaces, projective spaces and grassmannians in the ca\-te\-gory of ringed spaces. We show how finite posets and sheaves of rings on them appear in a natural way.
This paper is a contribution to the study of extensions of arbitrary models of ZF (Zermelo-Fraenkel set theory), with no regard to countability or well-foundedness of the models involved. We present some new constructions of certain types…
We describe explicitly how certain standard opens of the Hilbert scheme of points are embedded into Grassmannians. The standard opens of the Hilbert scheme that we consider are given as the intersection of a corresponding basic open affine…
This is the last version of AG/0111277. Here the old abstract: We define $\epsilon$-factors in the de Rham setting and calculate the determinant of the Gau\ss-Manin connection for a family of (affine) curves and a vector bundle equipped…
Some aspects of differential and integral calculi on generalized grassmann (paragrassmann) algebras are considered. The integration over paragrassmann variables is applied to evaluate the partition function for the $Z_{p+1}$ Potts model on…
A formulation for a non-trivial composition of two classical gauge structures is given: Two parent gauge structures of a common base space are synthesized so as to obtain a daughter structure which is fundamental by itself. The model is…
The goal of this paper is to explicitly describe in terms of generators and relations the universal central extension of the infinite dimensional Lie algebra, $\mathfrak{g} \otimes \mathbb{C}[t,t^{-1},u]$ with finite dimensional simple Lie…
We consider a family of generic weighted arrangements of $n$ hyperplanes in $\C^k$ and show that the Gauss-Manin connection for the associated hypergeometric integrals, the contravariant form on the space of singular vectors, and the…
By a grassmannian we understand a usual complex grassmannian or possibly an orthogonal or symplectic grassmannian. We classify, with few exceptions, linear embeddings of grassmannians into larger grassmannians, where the linearity…
For the simple Lie algebra $g = sl(n,C)$ we we find a set of generators and relations for the classical family algebra $(End(g)\otimes S(g))^G$ as an algebra over the ring $I(g)$. From these we can then determine a $I(g)$-linear basis of…
We evaluate several arctangent and logarithmic integrals depending on a parameter. This provides a closed form summation of certain series and also gives integral and series representation of some classical constants.
Infinite graphs are finitary in the sense that their points are connected via finite paths. So what would an infinitary generalization of finite graphs look like? Usually this question is answered with the aid of topology, e.g. in the case…
In analogy with the origin of the additive structure of $K$-theory, we construct an $E_\infty$ structure on the matroid Grassmannian (the space of oriented matroids) for which the underlying binary operation is the direct sum of matroids.…
We discuss a conjecture of Ingleton on excluded minors for base-orderability, and, extending a result he stated, we prove that infinitely many of the matroids that he identified are excluded minors for base-orderability, as well as for the…
In this note, we give explicit expressions of Gauss sums for general (resp. special) linear groups over finite fields, which involves Gauss sums (resp. Kloosterman sums). The key ingredient is averaging such sums over Borel subgroups. As…
In this note, we give Gysin formulas for partial flag bundles for the classical groups. We then give Gysin formulas for Schubert varieties in Grassmann bundles, including isotropic ones. All these formulas are proved in a rather uniform way…
We construct Grassmannian categories of infinite rank, providing an infinite analogue of the Grassmannian cluster categories introduced by Jensen, King, and Su. Each Grassmannian category of infinite rank is given as the category of graded…