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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 2

Example text

We give them in Table 1 and Table 2 with the data of intersections of codimension one among the irreducible Lagrangian subvarieties. The complex holonomy diagrams of Wls and 3K ( S l, S 2) are given in Figs. 1 and 2. They can be drawn from the data in Tables 1 and 2. Now we turn to the problem of the computation of fe-functions. As stated in [ S m - S h ] , the 6-function of complex powers of relatively invariant polynomials plays an important role when we construct the meromorphic extensions of the local zeta functions.

However we do not have many examples of calculations of the microlocal structure of relatively invariant hyperfunctions on non-irreducible regular prehomogeneous vector space. Above all, there are remarkable examples among them that raise different phenomena from the case of irreducible regular prehomogeneous vector spaces. They are prehomogeneous vector spaces whose group actions are by parabolic subgroups of reductive groups. Let ( G c , p , Vc) be a regular irreducible prehomogeneous vector space, where Gc is a connected reductive algebraic group.

Masani, The prediction theory of multivariate stochastic processes II, The linear Predictor, Acta. Math. 99 (1958) 93-137. New Local Supersymmetry in the Framework of Einstein Gravity Noboru Nakanishi Research Institute for Mathematical Kyoto University Kyoto, Japan 1. Sciences Quantum Field Theory Quantum field theory is the fundamental theory describing particle physics. , distributions or hyperfunctions) of spacetime χ . According to the statistics of particles, fields are classified into two kinds, Bosonic (commutation type) and Fermionic (anticommutation type).

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