Algebraic Analysis. Papers Dedicated to Professor Mikio Sato by Masaki Kashiwara, Takahiro Kawai

By Masaki Kashiwara, Takahiro Kawai

E-book through Kashiwara, Masaki

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Extra resources for Algebraic Analysis. Papers Dedicated to Professor Mikio Sato on the Occasion of his Sixtieth Birthday, Volume 2

Example text

T. Shintani, On zeta functions associated with the vector space of quadratic forms, J. Fac. Sei. Univ. Tokyo, SecIA 22, N o . 1 (1975) 25-65. F. Sato, Zeta functions in several variables associated with prehomogeneous vector spaces I, Tôhoku Math. J. 34 (1982) 437-483. Ε. Β. Vinberg, Complexity of actions of reductive groups, Functional Anal. Appl. 20, N o . 1 (1986) 1-13. Applications of Transformation Theory for Nonlinear Integrable Systems to Linear Prediction Problems and Isospectral Deformations Yoshimasa Nakamura Department of Mathematics Gifu University Gifu, Japan 1.

For general fceN, we formuXkeJf, Dke2 a n d Yk e late the Bruhat decomposition Mk = Xk( YkDk)~\ Jf, and the transformation from Lk to Lk+X by Lk+X = LkXk. Here the next l Mk+X is defined by Mk+X = LkixM0Lk+x. Observe that Mk+X = ( YkDk)~ Xk. 1) The main purpose of this section is to prove Theorem 2. systems. Spec Mk = Spec M 0 for keN x in terms of nonlinear l integrable It is easy to see det(X f c( YkDk)~ - λ ) = det(( YkDk)~ Xk - λ ) . Since invertible matrices are dense, this identity holds in general.

E. Witten, Supersymmetry and Morse theory, J. Diff. Geom. 17 (1982) 661-692. E. Witten, The index of Dirac operator in loop space, preprint, 1987. A Note on the Holonomic System of Invariant Hyperfunctions on a Certain Prehomogeneous Vector Space Masakazu M uro 1 Department of Mathematics Kochi University Kochi, Japan Introduction The theory of holonomic systems and microlocal analysis, which was originated by M. Sato and developed mainly by M. Sato and M. Kashiwara, has had great success in several areas of mathematics.

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