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...

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

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...

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

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

{\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...

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...

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

R n + 1 ) {\displaystyle \mathbf {Gr} (1,\mathbb {R} ^{n+1})} ⁠ of a Grassmannian space. As with all projective spaces, ⁠ R P n {\displaystyle \mathbb...

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

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...

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

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

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

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

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})}...

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...

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...

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

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}} ....

hypergeometric function is a function that is (more or less) defined on a Grassmannian, and depends on a choice of some complex numbers and signs. Gelfand,...

parametrized by points in a tube domain inside a complex Lagrangian Grassmannian, namely the Siegel upper half space. The most common form of theta function...

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

{\displaystyle \mathrm {S} (\mathrm {U} (p)\times \mathrm {U} (2))} p Grassmannian of complex 2-dimensional subspaces of C p + 2 {\displaystyle \mathbb...

{\text{Quot}}_{{\mathcal {E}}/X/S}^{\Phi }} over S {\displaystyle S} . The Grassmannian G ( n , k ) {\displaystyle G(n,k)} of k {\displaystyle k} -planes in...

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...

through the origin of V. That is, if V is n-dimensional, then P(V∗) is the Grassmannian of n − 1 planes in V. In algebraic geometry, this construction allows...