Complex Manifold Deformation Theory
6 Orbit of Word
Conjecture
Word has orbit.
[View¶]
¶Mathematics is a view in which I freely appreciate objects as if I see flowers, mountains and vigorous port towns at dawn.
1
Complex vector space that has Hermitian inner product V
Lie group of V U(V)
Connected closed Lie group G
Complexification of G GC
Coordinate ring of V A(V)
All the invariant of A(V) 's action to GC A(V)GC
Manifold defined by A(V)GC V//GC
2
Lattice M= Hom(GC, C*)
Dual lattice M*
x = t(1, ..., 1)
V
(Theorem)
Necessary and sufficient condition that orbit GCx is closed is that σ = M
R
is satisfied.
σ is rational polyhedral convex cone defined by one-parameter subgroup and character of GC.
(Theorem)
Topological space of V//GC is quotient space that all the closed GC orbit is divided by equivalent relation.
3
gGC
Orbit of x gx
px(g) := ||gx||2
4
2n dimensional rational manifold X
Lie ring from X to G g
Dual space of g g*
Map
: X 
g*
5
(Theorem)
All the closed GC orbit of V is corresponded with
(0) / G one to one.
[Impression¶]
¶ Impression is developed from the view.
1
Language is supposed to be V.
Word is supposed to to be GC.
Meaning minimum is supposed to be x.
Meaning is supposed to be orbit of x.
Meaning has distance ||gx||2 .
2
and
are supposed to be
grammar of language.
3
Under the supposition, meaning and grammar are corresponded one to one by the theorem.
[References]
Orbit of language is an essential concept of Quantum Theory for Language group.
Especially refer to the next.
#1 Quantum Theory for Language Synopsis / Tokyo January 15, 2004
#2 Quantification of Quantum / Toky May 29, 2004
#3 Mirror Language / Tokyo June 10, 2004
#4 Prague Theory 3 / Tokyo January 28, 2005
Related with orbit, distance is also essential concept from early work on Quantum Theory for Language.
Espetially refer to the next.
#5 Distance Theory
Tokyo December 23, 2008
Sekinan Research Field of language
Back to sekinanlogoshome
[View¶]
¶Mathematics is a view in which I freely appreciate objects as if I see flowers, mountains and vigorous port towns at dawn.
1
Complex vector space that has Hermitian inner product V
Lie group of V U(V)
Connected closed Lie group G
Complexification of G GC
Coordinate ring of V A(V)
All the invariant of A(V) 's action to GC A(V)GC
Manifold defined by A(V)GC V//GC
2
Lattice M= Hom(GC, C*)
Dual lattice M*
x = t(1, ..., 1)
V(Theorem)
Necessary and sufficient condition that orbit GCx is closed is that σ = M
R
is satisfied.σ is rational polyhedral convex cone defined by one-parameter subgroup and character of GC.
(Theorem)
Topological space of V//GC is quotient space that all the closed GC orbit is divided by equivalent relation.
3
g
GCOrbit of x gx
px(g) := ||gx||2
4
2n dimensional rational manifold X
Lie ring from X to G g
Dual space of g g*
Map
: X g*5
(Theorem)
All the closed GC orbit of V is corresponded with
(0) / G one to one.[Impression¶]
¶ Impression is developed from the view.
1
Language is supposed to be V.
Word is supposed to to be GC.
Meaning minimum is supposed to be x.
Meaning is supposed to be orbit of x.
Meaning has distance ||gx||2 .
2
and
are supposed to be
grammar of language.3
Under the supposition, meaning and grammar are corresponded one to one by the theorem.
[References]
Orbit of language is an essential concept of Quantum Theory for Language group.
Especially refer to the next.
#1 Quantum Theory for Language Synopsis / Tokyo January 15, 2004
#2 Quantification of Quantum / Toky May 29, 2004
#3 Mirror Language / Tokyo June 10, 2004
#4 Prague Theory 3 / Tokyo January 28, 2005
Related with orbit, distance is also essential concept from early work on Quantum Theory for Language.
Espetially refer to the next.
#5 Distance Theory
Tokyo December 23, 2008
Sekinan Research Field of language
Back to sekinanlogoshome
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