Symmetry of Language
[Preparation]
3 dimensional manifold M
Level of affine Lie ring k
Topological invariant of M Zk(M)
Manifold having reverse orientation of M -M
<Theorem>
[Inerpretation]
Language is expressed by M.
Parameter of meaning is expressed by k.
Meaning of language is expressed by Zk(M).
Language has a symmetry by orientation.
When M is 3 dimensional spherical surface, Zk (S3) = S00.
Here,
At affine Lie ring level k, characteristic 
, 
,
The highest weight set of affine Lie ring's level k P+(k) ={0, 1, ..., k}
The highest weight of level k λ
The highest weight of level k at infinity η
[Supposition]
If langauge has a symmetry, there is a language's origin that the two orientations are oriented.
If language is 3 dimensional spheric surface, its meaning is 3 dimensional shperical surface with level k, the highest weight 0 and the highest weight at infinity 0.
[Refereneces]
(1)
(2)
(3)
<Trilogy>
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