In mathematics, the Grassmannian G r k ( V ) {\displaystyle \mathbf {Gr} _{k}(V)} (named in honour of Hermann Grassmann) is a differentiable manifold that...

In mathematics, the Lagrangian Grassmannian is the smooth manifold of Lagrangian subspaces of a real symplectic vector space V. Its dimension is 1/2n(n...

In mathematics, a Grassmannian may refer to: Affine Grassmannian Affine Grassmannian (manifold) Grassmannian, the classical parameter space for linear...

amplituhedron is defined as a mathematical space known as the positive Grassmannian. Amplituhedron theory challenges the notion that spacetime locality and...

In mathematics, there are two distinct meanings of the term affine Grassmannian. In one it is the manifold of all k-dimensional affine subspaces of Rn...

In mathematics, the affine Grassmannian of an algebraic group G over a field k is an ind-scheme—a colimit of finite-dimensional schemes—which can be thought...

1 ( x ) = G d ( E x ) {\displaystyle p^{-1}(x)=G_{d}(E_{x})} is the Grassmannian of the d-dimensional vector subspaces of E x {\displaystyle E_{x}} ....

space BU is the classifying space for stable complex vector bundles (a Grassmannian in infinite dimensions). One formulation of Bott periodicity describes...

point stabilizer general linear group): An = Aff(n, K) / GL(n, K). Grassmannian: Gr(r, n) = O(n) / (O(r) × O(n − r)) Topological vector spaces (in the...

the concept which is now known as a vector space. He introduced the Grassmannian, the space which parameterizes all k-dimensional linear subspaces of...

bundle is a vector bundle occurring over a Grassmannian in a natural tautological way: for a Grassmannian of k {\displaystyle k} -dimensional subspaces...

In mathematics, the Plücker map embeds the Grassmannian G r ( k , V ) {\displaystyle \mathbf {Gr} (k,V)} , whose elements are k-dimensional subspaces of...

projective homogeneous variety, known as the isotropic Grassmannian or orthogonal Grassmannian OGr(r + 1, n + 2). (The numbering refers to the dimensions...

give a concrete description of the Schubert cells associated with the Grassmannian of k {\displaystyle k} -dimensional subspaces of a vector space. If j...

R n + 1 ) {\displaystyle \mathbf {Gr} (1,\mathbb {R} ^{n+1})} of a Grassmannian space. As with all projective spaces, RPn is formed by taking the quotient...

space, which is roughly equivalent to describing the cohomology ring of Grassmannians. Sometimes it is used to mean the more general enumerative geometry...

either a compact simple Lie group, a Grassmannian, a Lagrangian Grassmannian, or a double Lagrangian Grassmannian of subspaces of ( A ⊗ B ) n , {\displaystyle...

the Grassmannian of n-planes in an infinite-dimensional complex Hilbert space; or, the direct limit, with the induced topology, of Grassmannians of n...

of algebraic curves). Let V be a finite-dimensional vector space. The Grassmannian variety Gn(V) is the set of all n-dimensional subspaces of V. It is a...

Grassmann number Grassmann variables Grassmannian Affine Grassmannian Affine Grassmannian (manifold) Lagrangian Grassmannian Grassmann–Cayley algebra Grassmann–Plücker...

to the Schubert decomposition of the Grassmannian, and are q-analogs of the Betti numbers of complex Grassmannians. This was one of the clues leading to...

Gauss map can also be defined, and its target space is the oriented Grassmannian G ~ k , n {\displaystyle {\tilde {G}}_{k,n}} , i.e. the set of all oriented...

field with q elements; i.e. it is the number of points in the finite Grassmannian G r ( k , F q n ) {\displaystyle \mathrm {Gr} (k,\mathbb {F} _{q}^{n})}...

SU(p,q), A III 2pq Hermitian. Grassmannian of p subspaces of Cp+q. If p or q is 2; quaternion-Kähler Hermitian. Grassmannian of maximal positive definite...

complex lines in Cn+1 passing through the origin. More generally, the Grassmannian G(k, V) of a vector space V over a field F is the moduli space of all...

Institutions University of Manchester University of Cambridge Thesis Grassmannian Varieties / The Conic as a Space Element  (1932) Doctoral advisor H.F...

tropical geometry, algebraic combinatorics, amplituhedra, and the positive Grassmannian. She is Dwight Parker Robinson Professor of Mathematics at Harvard University...

algebraic geometry, a Schubert variety is a certain subvariety of a Grassmannian, G r k ( V ) {\displaystyle \mathbf {Gr} _{k}(V)} of k {\displaystyle...

underlying vector space of dimension 4. It is now part of the theory of Grassmannians G r ( k , V ) {\displaystyle \mathbf {Gr} (k,V)} ( k {\displaystyle...

{\displaystyle Gr_{n}(V)} denote the Grassmannian, the space of n-dimensional linear subspaces of V, and denote the infinite Grassmannian G r n = G r n ( R ∞ ) {\displaystyle...