Publications of the Research Institute for Mathematical Sciences

Propagation of the Irregularity of a Microdifferential System

Teresa Monteiro Fernandes

2001 Volume 37 Issue 2 Pages 119-139
Published: 2001
Released on J-STAGE: April 24, 2009

DOIhttps://doi.org/10.2977/prims/1145476846

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We construct the functor of microlocal analytic irregularity Iμ hom(·, \mathcal{O}_X) which gives a natural third term of a distinguished triangle associated to the transformation tμ hom(·, \mathcal{O}_X)→μ hom(·, \mathcal{O}_X) of functors on the derived category of \mathbb{R}-constructible sheaves. When restricting to \mathbb{C}-constructible objects we prove that the microlocal irregularity of a microdifferential system propagates along non 1-microcharacteristic directions, as a consequence of the propagation for tμ hom(·, \mathcal{O}_X) and μ hom(·, \mathcal{O}_X).

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Analytic Representation of Generalized Tempered Distributions by Wavelets

Byung Keun Sohn, Dae Hyeon Pahk

2001 Volume 37 Issue 2 Pages 141-149
Published: 2001
Released on J-STAGE: April 24, 2009

DOIhttps://doi.org/10.2977/prims/1145476847

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The analytic representation of the generalized tempered distributions of exponential growth, \mathcal{K}_p^r', is given in terms of series of analytic wavelets. These series converge uniformly on compact subsets of the upper and lower half planes.

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On the Micro-Hyperbolic Boundary Value Problem for Systems of Differential Equations

Motoo Uchida

2001 Volume 37 Issue 2 Pages 151-163
Published: 2001
Released on J-STAGE: April 24, 2009

DOIhttps://doi.org/10.2977/prims/1145476848

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We formulate the boundary value problem for systems of linear differential equations which satisfy a certain condition of micro-hyperbolicity at the boundary in the same way as the Kashiwara-Kawai formulation for elliptic systems.

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On a Conjecture of Kac-Wakimoto

Feng Xu

2001 Volume 37 Issue 2 Pages 165-190
Published: 2001
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.2977/prims/1145476849

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We prove a conjecture about mininmal index of certain representations of Coset Algebraic Conformal Field Theories under certain conditions as formulated previously by us. As a by-product, the Kac-Wakimoto Conjecture (KWC) which is related to the asympotics of the coset characters is true under the same conditions. The same idea in the proof also proves a recent conjecture related to subfactors from conformal inclusions.

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G-surgery on 3-dimensional Manifolds for Homology Equivalences

Masaharu Morimoto

2001 Volume 37 Issue 2 Pages 191-220
Published: 2001
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.2977/prims/1145476850

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For a finite group G and a G-map f : X → Y of degree one, where X and Y are compact, connected, oriented, 3-dimensional, smooth G-manifolds, we give an obstruction element σ(f) in a K-theoretic group called the Bak group, with the property: σ(f)=0 guarantees that one can perform G-surgery on X so as to convert f to a homology equivalence f' : X' → Y. Using this obstruction theory, we determine the G-homeomorphism type of the singular set of a smooth action of A₅ on a 3-dimensional homology sphere having exactly one fixed point, where A₅ is the alternating group on five letters.

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Hartogs' Phenomena for Microfunctions with Holomorphic Parameters

Otto Liess, Yasunori Okada, Nobuyuki Tose

2001 Volume 37 Issue 2 Pages 221-238
Published: 2001
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.2977/prims/1145476851

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