Related papers: Morphisms between Grassmannians

Let $\mathcal A$ and $\mathcal B$ be two (complex) algebras. A linear map $\phi:{\mathcal A}\to{\mathcal B}$ is called $n$-homomorphism if $\phi(a_{1}... a_{n})=\phi(a_{1})...\phi(a_{n})$ for each $a_{1},...,a_{n}\in{\mathcal A}.$ In this…

Let G=GL(n,F) where F is a local field of arbitrary characteristic, and let $\pi_1,\pi_2$ be representations induced from characters of two maximal parabolic subgroups $P_1,P_2$. We explicitly determine the space $Hom_G(\pi_1,\pi_2)$ of…

Let $\Gamma_{k}(V)$ be the Grassmann graph formed by $k$-dimensional subspaces of an $n$-dimensional vector space over the finite field ${\mathbb F}_{q}$ consisting of $q$ elements and $1<k<n-1$. Denote by $\Gamma(n,k)_q$ the restriction of…

We construct a non-commutative version of the Grassmann variety $G(2,4)$ as a non-commutative moduli space of linear subspaces in a projective space.

Flag manifolds are shown to describe the relations between configurations of distinguished points (topologically equivalent to punctures) embedded in a general spacetime manifold. Grassmannians are flag manifolds with just two subsets of…

Let $k$ be an algebraically closed field and ${\sf G}(2,k^4)$ the Grassmannian of 2-planes in $k^4$. We associate to each 6-dimensional subspace $R$ of the space of 4x4 matrices over $k$ a closed subscheme ${\bf X}_R \subseteq {\sf…

We study the problem of classifying the holomorphic $(m,n)$-subharmonic morphisms in complex space. This determines which holomorphic mappings preserves $m$-subharmonicity in the sense that the composition of the holomorphic mapping with a…

Let $H$ be a complex Hilbert space and let ${\mathcal G}_{k}(H)$ be the Grassmannian formed by $k$-dimensional subspaces of $H$. Suppose that $\dim H>2k$ and $f$ is an orthogonality preserving injective transformation of ${\mathcal…

We show that the transformations of Grassmannians (of complex Hilbert spaces) induced by linear or conjugate-linear isometries can be characterized as transformations preserving some of principal angles (corresponding to the orthogonality,…

Integrable flows on the Grassmannians Gr(N-1,N+1) are defined by the requirement of closedness of the differential N-1 forms $\Omega_{N-1}$ of rank N-1 naturally associated with Gr(N-1,N+1). Gauge-invariant parts of these flows, given by…

Let G(d,n) denote the Grassmannian of d-planes in C^n and let T be the torus (C^*)^n/diag(C^*) which acts on G(d,n). Let x be a point of G(d,n) and let \bar{Tx} be the closure of the T-orbit through x. Then the class of the structure sheaf…

We consider the Grassmannian $\mathbb{G}r(k,n)$ of $(k+1)$-dimensional linear subspaces of $V_n=H^0({\P^1},\O_{\P^1}(n))$. We define $\frak{X}_{k,r,d}$ as the classifying space of the $k$-dimensional linear systems of degree $n$ on $\P^1$…

We construct the Gromov-Witten invariants of moduli of stable morphisms to $\Pf$ with fields. This is the all genus mathematical theory of the Guffin-Sharpe-Witten model, and is a modified twisted Gromov-Witten invariants of $\Pf$. These…

We study linear projections on Pluecker space whose restriction to the Grassmannian is a non-trivial branched cover. When an automorphism of the Grassmannian preserves the fibers, we show that the Grassmannian is necessarily of…

Let $G$ be a graph with vertex set $V(G)$, $f$ a permutation of $V(G)$. Define $\delta_f(G)=|d(x,y)-d(f(x),f(y))|$ and $\delta_f(G)=\Sigma\delta_f(x,y)$, where the sum is taken over all unordered pair $x$, $y$ of distinct vertices of $G$.…

Symmetric $k$-varieties generalize Riemannian sym\-me\-tric spaces to reductive groups defined over arbitrary fields. For most perfect fields, it is known that symmetric $k$-varieties are in one-to-one correspondence with isomorphy classes…

Recent developments in particle physics have revealed deep connections between scattering amplitudes and tropical geometry. From the heart of this relationship emerged the chirotropical Grassmannian $\text{Trop}^\chi \text{G}(k,n)$ and the…

For an arbitrary field of any characteristic we give an explicit description, in terms of Pl\"ucker coordinates, of the projective linear space that cuts out the Lagrangian-Grassmannian variety $L(n,2n)$ of maximal isotropic subspaces in a…

In this paper we define a generalization of the pentagram map to a map on twisted polygons in the Grassmannian space Gr(n;mn). We define invariants of Grassmannian twisted polygons under the natural action of SL(nm), invariants that define…

Let F be a field and i < j be integers between 1 and n. A map of Grassmannians f : Gr(i, F^n) --> Gr(j, F^n) is called nesting, if l is contained in f(l) for every l in Gr(i, F^n). We show that there are no continuous nesting maps over C…