Scouting Federation of Portugal

Roads in Digby County, Nova Scotia

Szczepaniak
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Snowdon Beetle

Symplectic representation

Snowdon beetle

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Australian Capital Territory Emergency Services Authority

Malaysian JKR roads 109

Rainbow Leaf Beetle

Soukhane

Rainbow leaf beetle

Buik of King Alexander the Conquerour

Gondet

In mathematical field of representation theory, a symplectic representation is a representation of a group or a Lie algebra on a symplectic vector space (V, ω) which preserves the symplectic form ω. Here ω is a nondegenerate skew symmetric bilinear form ω : V × V → F {\displaystyle \omega \colon V\times V\to \mathbb {F} } where F is the field of scalars.

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Smart For Life

Roads in Shelburne County, Nova Scotia

Oldtimers disease

In mathematical field of representation theory, a symplectic representation is a representation of a group or a Lie algebra on a symplectic vector space (V, ω) which preserves the symplectic form ω. Here ω is a nondegenerate skew symmetric bilinear form ω : V × V → F {\displaystyle \omega \colon V\times V\to \mathbb {F} } where F is the field of scalars. A representation of a group G preserves ω if ω ( g ⋅ v , g ⋅ w ) = ω ( v , w ) {\displaystyle \omega (g\cdot v,g\cdot w)=\omega (v,w)} for all g in G and v, w in V, whereas a representation of a Lie algebra g preserves ω if ω ( ξ ⋅ v , w ) + ω ( v , ξ ⋅ w ) = 0 {\displaystyle \omega (\xi \cdot v,w)+\omega (v,\xi \cdot w)=0} for all ξ in g and v, w in V. Thus a representation of G or g is equivalently a group or Lie algebra homomorphism from G or g to the symplectic group Sp(V,ω) or its Lie algebra sp(V,ω)If G is a compact group (for example, a finite group), and F is the field of complex numbers, then by introducing a compatible unitary structure (which exists by an averaging argument), one can show that any complex symplectic representation is a quaternionic representation. Quaternionic representations of finite or compact groups are often called symplectic representations, and may be identified using the Frobenius-Schur indicator.

USS Sgt. Andrew Miller

Languages of Gujarat

GothiaTek

Sbaiz
1965–66 Coupe de France

Rhythm method

TV 23

Valere Sinitsin

Karakhanbeyli

The Buik of Alexander the Conquerour

TV 42