By Masaki Kashiwara, Takahiro Kawai
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Extra resources for Algebraic Analysis. Papers Dedicated to Professor Mikio Sato on the Occasion of his Sixtieth Birthday, Volume 1
L. Yan, Phys. Lett. 123A (1987) 219.  The case N = 4 is treated in B. M. McCoy, J. H. H. Perk, S. Tang, and C. H. Sah, Phys. Lett. 125 A (1987) 9.  R. J. Baxter, Phys. Rev. Lett. 26 (1971) 832; Ann. Phys. 70 (1972) 193.  See, for example, V. I. Arnol'd, Usp. Mat. Nauk 18, No. 6 (1963) 91 [Russian Mathematical Surveys 18, 6 (1963) 85].  B. M. McCoy and T. T. Wu, Nuovo Cimento 56B (1968) 311; B. Sutherland, J. Math. Phys. 11 (1970) 3183; L. Onsager, in Critical Phenomena in Alloys, Magnets, and Supercon ductors (R.
The most detailed statement of the result is that the Ising model is related to a free fermion theory on a lattice. This connection was first shown by Kaufman  and has deeply influenced all subsequent discussions. It is widely believed that for the ZN model with b = \ there is also some sort of free theory of "parafermions" underlying the model and in an appropriate continuum limit an impressive number of results have been derived using the conformai field theory approach [14,15]. Unfortunately, no one has been able to replicate Kaufman's analysis on the lattice for Af > 3 , because, even though the basic definition of fermions may be generalized to parafermions , the resulting objects do not seem to obey linear equations on the lattice.
We restrict our discussion to local solvability, for our main interest is in the case of variable coefficients. Theorem 1 is proved using functional analysis. Let us remark that the stalk 0$ is a DFS-space (, ) and its dual is isomorphic to ^ ^ } | C % the space of holomorphic hyperfunctions (, ). We will abbreviate ®T*}\c" to 39°°. , of order 1, minimal type). Here the topology of E0(C") is given by the family of norms \\φ\\ε =sup|
0 ) . Οχ^ϋχ, it suffices to show the following: (a) The image of P : 0$ -> (9* is dense.
Algebraic Analysis. Papers Dedicated to Professor Mikio Sato on the Occasion of his Sixtieth Birthday, Volume 1 by Masaki Kashiwara, Takahiro Kawai
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