Related papers: Morphisms between Grassmannians, II

We realise the Bott-Samelson resolutions of type A Schubert varieties as quiver Grassmannians. In order to explicitly describe this isomorphism, we introduce the notion of a \textit{geometrically compatible} decomposition for any…

We show that modeling a Grassmannian as symmetric orthogonal matrices $\operatorname{Gr}(k,\mathbb{R}^n) \cong\{Q \in \mathbb{R}^{n \times n} : Q^{\scriptscriptstyle\mathsf{T}} Q = I, \; Q^{\scriptscriptstyle\mathsf{T}} = Q,\;…

A demonstration is given that the simplest model of quantum mechanics formulated on a plane non-commutative geometry endowed with a Galilean symmetry group in which the position and linear momentum-variable commutators are first order in…

Let $n=4k+1$ and $k\geq 4$. We show that there exists maximal commutative subalgebras (with respect to inclusion) of dimension less that $3\cdot 2^{n-2}$.

The pairs $(\mathcal{D},G)$, where $\mathcal{D}$ is a non-trivial $2$-$(k^{2},k,\lambda )$ design, with $\lambda \mid k$, and $G$ is a flag-transitive automorphism group of $\mathcal{D}$ of affine type such that $G \nleq A \Gamma…

Let $\varphi$ and $\varphi'$ be two homotopic actions of the topological group $G$ on the topological space $X$. To an object $A$ in the $G$-equivariant derived category $D_{\varphi}(X)$ of $X$ relative to the action $\varphi$ we associate…

In previous work, we defined extended versions of von Neumann dimension for Banach space representations of sofic groups. The main application was a definition of l^{p}-dimension and, using this, a proof that the actions of a countable…

Let d_{k,n} and #_{k,n} denote the dimension and the degree of the Grassmannian G_{k,n} of k-planes in projective n-space, respectively. For each k between 1 and n-2 there are 2^{d_{k,n}} \cdot #_{k,n} (a priori complex) k-planes in P^n…

We construct all possible noncommutative deformations of a Kleinian singularity ${\mathbb C}^2/\Gamma$ of type $D_n$ in terms of generators and relations, and solve the problem of when two deformations are isomorphic. We prove that all…

In this paper we use toric geometry to investigate the topology of the totally non-negative part of the Grassmannian (Gr_{kn})_{\geq 0}. This is a cell complex whose cells Delta_G can be parameterized in terms of the combinatorics of…

We define the notion of a smooth pseudo-Riemannian algebraic variety $(X,g)$ over a field $k$ of characteristic $0$, which is an algebraic analogue of the notion of Riemannian manifold and we study, from a model-theoretic perspective, the…

This paper shows that the Grassmann Manifolds $G_{\bf F}(n,N)$ can all be imbedded in an Euclidean space $M_{\bf F}(N)$ naturally and the imbedding can be realized by the eigenfunctions of Laplacian $\triangle$ on $G_{\bf F}(n,N)$. They are…

Let $X$ be a compact Riemann surface of genus 2 and $D$ a very ample divisor with $\phi_D$ its associated embedding into $\mathbb{P}^{n}$. We consider the set $G_{X,D}$ of linear subspaces $W$ of $\mathbb{P}^n$ of codimension $2$ with…

We prove that for any k greater or equal to 2, given a smooth compact k-dimensional manifold and a multiplicative k-1-gerbe on a Lie group, together with an integrable connection, there is a line bundle on the corresponding…

We define a nonnegative integer $\la(L,L_0;\phi)$ for a pair of diffeomorphic closed Lagrangian surfaces $L_0,L$ embedded in a symplectic 4-manifold $(M,\w)$ and a diffeomorphism $\phi\in\Diff^+(M)$ satisfying $\phi(L_0)=L$. We prove that…

l-Conformal Galilei algebra, denoted by g{l}{d}, is a non-semisimple Lie algebra specified by a pair of parameters (d,l). The algebra is regarded as a nonrelativistic analogue of the conformal algebra. We derive hierarchies of partial…

We study a family $C_{s,l}$ of Capelli-type invariant differential operators on the space of rectangular matrices over a real division algebra. The $C_{s,l}$ descend to invariant differential operators on the corresponding Grassmannian,…

Given two nilpotent endomorphisms, we determine when their lattices of hyperinvariant subspaces are isomorphic. The study of the lattice of hyperinvariant subspaces can be reduced to the nilpotent case when the endomorphism has a…

The Grassmann manifold G_{n,p}(L) is the set of all p-dimensional planes (through the origin) in the n-dimensional Euclidean space L^{n}, where L is either R or C. This paper considers an unequal dimensional quantization in which a source…

We describe an iterative construction of Lagrangian tori in the complex Grassmannian $\operatorname{Gr}(k,n)$, based on the cluster algebra structure of the coordinate ring of a mirror Landau-Ginzburg model proposed by Marsh-Rietsch. Each…