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Type of vector space in mathematics
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
Lagrangian_Grassmannian
Mathematical space
as Isotropic Grassmannians or Lagrangian Grassmannians . Isotropic Grassmannian Lagrangian Grassmannian Grassmannians provide classifying spaces in K-theory
Grassmannian
Λ ( V ) {\displaystyle \Lambda (V)} denote its Lagrangian Grassmannian, the manifold of all Lagrangian subspaces of V {\displaystyle V} . The topology
Maslov_index
Topics referred to by the same term
space for linear subspaces of a linear space or projective space Lagrangian Grassmannian Grassmann algebra, or exterior algebra, a setting where the exterior
Grassmannian_(disambiguation)
Describes a periodicity in the homotopy groups of classical groups
space BU is the classifying space for stable complex vector bundles (a Grassmannian in infinite dimensions). One formulation of Bott periodicity describes
Bott_periodicity_theorem
Paris [fr]. Lagrangian analysis Lagrangian coordinates Lagrangian derivative Lagrangian drifter Lagrangian foliation Lagrangian Grassmannian Lagrangian intersection
List of things named after Joseph-Louis Lagrange
List_of_things_named_after_Joseph-Louis_Lagrange
Special functions of several complex variables
functions are parametrized by points in a tube domain inside a complex Lagrangian Grassmannian, namely the Siegel upper half space. One example of a theta function
Theta_function
(pseudo-)Riemannian manifold whose geodesics are reversible
either a compact simple Lie group, a Grassmannian, a Lagrangian Grassmannian, or a double Lagrangian Grassmannian of subspaces of ( A ⊗ B ) n , {\displaystyle
Symmetric_space
Grassmann number Grassmann variables Grassmannian Affine Grassmannian Affine Grassmannian (manifold) Lagrangian Grassmannian Grassmann–Cayley algebra Grassmann–Plücker
List of things named after Hermann Grassmann
List_of_things_named_after_Hermann_Grassmann
Relation between Lie algebras depicted as a square
either a compact simple Lie group, a Grassmannian, a Lagrangian Grassmannian, or a double Lagrangian Grassmannian of subspaces of ( A ⊗ B ) n , {\displaystyle
Freudenthal_magic_square
Type of group in mathematics
thinking of it as the fundamental group π1(U/O) of the stable Lagrangian Grassmannian as U/O ≅ Ω7(KO), so π1(U/O) = π1+7(KO). The orthogonal group anchors
Orthogonal_group
Space of complex matrices with positive definite imaginary part
vector space of symmetric matrices. The Shilov boundary is the Lagrangian Grassmannian Λ ( 2 g ) {\displaystyle \Lambda (2g)} . Geometrically, H g {\displaystyle
Siegel_upper_half-space
Nonlinear differential operator used to study conformal mappings
\operatorname {ev} _{t}} is a Lagrangian subspace of X {\displaystyle X} , and so the kernel defines a curve in the Lagrangian Grassmannian of ( X , ω ) {\displaystyle
Schwarzian_derivative
Analyzes the topology of a manifold by studying differentiable functions on that manifold
Combinatorial approach of studying the topology of a manifold Jacobi set Lagrangian Grassmannian – Type of vector space in mathematics Lusternik–Schnirelmann category –
Morse_theory
dimension 2n. Maslov index (sort of an intersection number defined on Lagrangian Grassmannian.) moment Moser's trick Novikov Novikov ring Poisson 1. 2. Poisson
Glossary of symplectic geometry
Glossary_of_symplectic_geometry
), the Shilov boundary can be identified with the Lagrangian Grassmannian, the space of Lagrangian subspaces in a real symplectic vector space. In the
Shilov_boundary
n-dimensional subspace U is called Lagrangian if B vanishes on U. The Lagrangian subpaces form a closed subset of the Grassmannian on which the complex symplectic
Invariant_convex_cone
Superconformal Yang–Mills theory
supersymmetric Yang–Mills (SYM) theory is a relativistic conformally invariant Lagrangian gauge theory describing the interactions of fermions via gauge field exchanges
N = 4 supersymmetric Yang–Mills theory
N_=_4_supersymmetric_Yang–Mills_theory
Property of certain dynamical systems
within the Grassmannian, and the Hirota equations as expressing the Plücker relations, characterizing the Plücker embedding of the Grassmannian in the projectivization
Integrable_system
American mathematician (born 1965)
Robin Hartshorne with a thesis on the surfaces in the four-dimensional Grassmannian. From 1990 to 1993 he was an assistant professor at the University of
Mark_Gross_(mathematician)
American mathematician and professor
Society, 259–271. with Tamvakis, H (2003). Quantum cohomology of the Lagrangian Grassmannian. Journal of Algebraic Geometry, 12(4):777-810. with Edidin, D;
Andrew_Kresch
Configurations of a system that do or do not satisfy classical equations of motion
Arkani-Hamed, N. (Dec 21, 2012). "Scattering Amplitudes and the Positive Grassmannian". arXiv:1212.5605 [hep-th]. Srednicki, Mark (2007). Quantum Field Theory
On_shell_and_off_shell
Riemannian manifold equipped with a differential p-form
equality. For x in M, set Gx(φ) to be the subset of such planes in the Grassmannian of p-planes in TxM. In cases of interest, Gx(φ) is always nonempty. Let
Calibrated_geometry
Branch of mathematics
important role played by its analytic methods. In wireless communications, Grassmannian manifolds are used for beamforming techniques in multiple antenna systems
Differential_geometry
Mathematics timeline
calculus, a branch of intersection theory taking place on the complex Grassmannian manifolds. 1902 David Hilbert Tentative axiomatisation (topological spaces
Timeline_of_manifolds
Discrete dynamical system on polygons in the projective plane and on their moduli space
m\geq 1} be integers. The pentagram map can also be generalized to the Grassmannian space G r ( m , m d ) {\displaystyle \mathrm {Gr} (m,md)} , which consists
Pentagram_map
Differential variety
{\displaystyle E} and for k = 1 {\displaystyle k=1} one recovers the Grassmannian of n {\displaystyle n} -dimensional subspaces of T E {\displaystyle TE}
Diffiety
History of maths
in terms of spherical perverse sheaves (or D-modules) on the affine Grassmannian GrG = G((t))/G[[t]] of the original group G. 2008 Ieke Moerdijk-Clemens
Timeline of category theory and related mathematics
Timeline_of_category_theory_and_related_mathematics
Interdisciplinary field of biology
coordinate systems via coordinate transformations as generated via the Lagrangian and Eulerian velocities of flow in R 3 {\displaystyle {\mathbb {R} }^{3}}
Computational_anatomy
acts freely on it. The quotient is the symplectic Grassmannian M consisting of n-dimensional Lagrangian subspaces of C2n. Define a map of A2 into M by sending
Mutation_(Jordan_algebra)
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LAGRANGIAN GRASSMANNIAN