By Masaki Kashiwara, Takahiro Kawai
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Additional info for Algebraic Analysis. Papers Dedicated to Professor Mikio Sato on the Occasion of his Sixtieth Birthday, Volume 2
0 , 1 ) (2) L l c: = p ( P c ) - ' ( 0 , . . ,0) L2C:=p(Pc) r / : : (4) L 3 C: = p ( P c ) - ( 0 , l , v (5) L 4 C: = p ( P c ) - ' ( l , 0 , . . , 0 ) (6) L 5 C: = p ( P c ) - ' ( 0 , . . ,0) are the unions of the following Pc-orbits. SoC ~ ^OC ^ ^ 2 C Sic ^3C (4) = = ^1C ^ ^3C ^ ^4C L5C We Λαυβ ifte same orbital decomposition by the contragredient rep- resentation p * . The proof of this Proposition is not difficult so we omit it. 2) (2) ch(SR ( S l. S 2 )) = U r t c V c . j = 0 We denote by EiC the closure T%iCVc (i = 0 , 1 , 2 ) a n d by AjC the closure T*jCVc 0 = 0, 1, 2, 3, 4, 5).
M. Maluse, Solvability of the super-KP equation and a generalization of the Birkhoff decomposition, Invent. Math. 92 (1988) 1-46. Yu. I. Manin and A. O. Radul, A supersymmetric extension of the KadomtsevPetviashvili hierarchy, Comm. Math. Phys. 98 (1985) 65-77. M. Sato and Y. Sato, Soliton equations as dynamical systems on infinite dimensional Grassmann manifold, Lect. Notes in Num. Appl. Anal. 5 (1982) 259-271. F. Schottky, Zur Theorie der Abelschen Functionen von vier Variablen, J. Reine undAngew.
We have maps Τ 3 t ^ S( t) e Gr 3 S τ ( 5 ) e C. Let τ ( 0 = T ( S ( 0 ) b e the composition of the above maps. ). but the τ-function solution of the K P system: r(x, t) = r ( x + t2, Now let us describe the Virasoro action on Gr. The Virasoro algebra V is a special central extension of the algebra g of vector fields on the circle 1 S . The g-action on a point of Gr produces an infinitesimal deformation of the complex structure of the corresponding curve. Let C be the curve l corresponding to a point S of Gr.
Algebraic Analysis. Papers Dedicated to Professor Mikio Sato on the Occasion of his Sixtieth Birthday, Volume 2 by Masaki Kashiwara, Takahiro Kawai