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

By Masaki Kashiwara, Takahiro Kawai

ISBN-10: 0124004660

ISBN-13: 9780124004665

Publication through Kashiwara, Masaki

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Read or Download Algebraic Analysis. Papers Dedicated to Professor Mikio Sato on the Occasion of his Sixtieth Birthday, Volume 2 PDF

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

Example text

Any locally symmetric part of the action is manifestly BRS invariant, but BRS invariance admits the addition of a 3 gauge-fixing plus FP-ghost part, which explicitly breaks the local symmetry. 4 The choice of gauge fixing is rather arbitrary, but it is preferable to preserve the global version of the original local symmetry. Once gauge fixing is set u p , the FP-ghost part is uniquely determined by the requirement of BRS invariance. The BRS invariance of the action implies the existence of a nilpotent BRS generator, which consistently defines a subsidiary condition [ 7 , 1 1 ] .

Sato and developed mainly by M. Sato and M. Kashiwara, has had great success in several areas of mathematics. In particular, we cannot do anything in the calculus of invariant hyperfunctions on prehomogeneous vector spaces without microlocal analysis. The microlocal structure of invariant holonomic systems and invariant hyperfunctions has been finely described in some papers in the case of irreducible regular prehomogeneous vector spaces on which reductive groups act, in connection with the computation of functional equations of zeta functions associated 1 This research is partially supported by Grant-in-Aid for Scientific Research 62740098 of Ministry of Education in Japan.

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).

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Algebraic Analysis. Papers Dedicated to Professor Mikio Sato on the Occasion of his Sixtieth Birthday, Volume 2 by Masaki Kashiwara, Takahiro Kawai

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