Linguistic Note 6 Orbit Space / July 24, 2007

Linguistic Note

6

Orbit Space

　　TANAKA Akio

1

Group     G

Set     X

x ∈ X

Orb( x ) = { σ. x ∈ X | σ∈G }

x’s stabilizer     G_x

Gx = { σ∈ G | σ. x = x }

X’s orbit space on operation G     G \ X

2

x ∈ X

Mapping     f :  G → Orb ( x )   f ( σ) = σ. x    σ∈ G

ξ ∈ G_x

ξ.x = x

f ( σG_x ) → f (σ)    σ∈G

f : G / G_x → Orb ( x )

G’s orbit on operation X is unique.

[Note]

Orbit may be helpful to quantum’s movement on Quantum Theory for Language.

[References]

Sending and Receiving Information on Quantum   Tokyo October 22, 2004

Changeability     Tokyo January 8, 2005

Individuality     Tokyo January 10, 2005

Frame-Quantum Theory     Tokyo March 13, 2005

Language and Spacetime     Time Flow in Word     Tokyo May 3, 2007

Tokyo July 24, 2007

Sekinan Research Field of Language