[geometry-ml:05354] 岡数学研究所セミナ−(9/25)のご案内【更新】

[matsuzawa]

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松澤淳一
〒630-8506 奈良市北魚屋西町
奈良女子大学　岡数学研究所　
Phone: 0742-20-3361 (研究室)
FAX: 0742-20-3367 (事務室）
matsuzawa ＠ cc.nara-wu.ac.jp

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Seminar in Oka Mathematical Institute

日時    9月25日（月）
場所   奈良女子大学理学系Ｂ棟4階　B1403（第3セミナー室）

Speakers and Titles
10 : 30 − 11 : 30
Boris Doubrov( Belarus State University)
Equivalence of bracket-generating vector distributions via control theory 

13 : 30 − 14 : 30
Toshihisa Kubo( Ryukoku University)
On the equivariant differential operators for SL(3,R) with maximal parabolic subgroup 

15 : 00 − 16 : 00
Masanori Adachi(Shizuoka University)
A review on Levi-flat hypersurfaces and Bergman spaces


 Abstracts
 B. Doubrov
T itle: Equivalence of bracket-generating vector distributions via control
theory
A bstract: We canonically associate a pseudo-product structure with any
bracket-generating distribution. Under some additional non-degeneracy
 conditions one can use the linearization principle and study these struc- 
tures via systems of linear ODEs whose solution space possesses an
 invari- ant symplectic form, The symbol of such linear systems is described
 by a homogeneous element of degree -1 in the Lie algebra sp(2n, R) equipped 
with an arbitrary parabolic grading. We show how such elements can be ef- 
fectively classified. In case of (2,3,5) distributions this construction leads to 
a pseudo-product structure modeled by the parabolic homogeneous space 
G2/B where B is the Borel subgroup.

 T.Kubo
Title: On the equivariant differential operators for SL(3,R) with maximal
parabolic subgroup
Abstract: Let  G ⊃ P be a real simple Lie group and a parabolic sub- group, 
respectively. For finite dimensional representations Vi (i = 1, 2) of P , 
let Vi → G/Pdenote the G-equivariant homogeneous vector bun-dle
 Vi over G/P with fiber Vi. Differentialoperators D : C∞(G/P, V1) → C∞(G/P, V2) 
are said to be equivariant (or covariant orintertwining) if D is equivariant under 
the actions of G on C∞(G/P, Vi) (i = 1, 2). A classicalexample of such an
 operator is the wave operator □3,1 on the Minkowski space R3,1 of 
signature (3, 1). Equivariant differential operators are impor- tant objects
 in both representation theory and parabolic geometry. In this talk we shall
 discuss a classification and explicit construction of equivariant differential 
operators for the following setting:(G, P ; V1, V2) = (SL(3, R), P1,2; Fn, Fm).
 Here, P1,2 is the maximal parabolic subgroup corresponding to the partition
 (1, 2), and Fn(resp. Fm) is the finite dimensional irreducible representation 
of P1,2 of dimension n (resp. m). This is based on joint work in progress  with 
Bent Orsted.
               M.  Adachi
Title: A review on Levi-flat hypersurfaces and Bergman spaces
Abstract:  A smooth real hypersurface in a complex manifold is said to be
 Levi-flat if its Levi form vanishes identically. In contrast to strictly pseudoconvex
 real hypersurfaces, where CR structure induces contact structure, Levi-flat 
hypersurfaces are endowed with foliations and their dynamical properties govern 
the behavior of holomorphic functions on the domains bounded by these hypersurfaces.
  A central topic in the study of Levi-flat hypersurfaces is the non-existence
problem of Levi-flat hypersurface in the complex projective plane. In my old work 
with Brinkschulte, we tried an approach to this problem via the study of Bergman
 spaces on the complement of the hypothetical  Levi-flat hypersurface. In this talk, 
after reviewing this attempt,  I would like to explain my computational result on the
 structure of  Bergman spaces of domains bounded by the unit tangent bundle of 
 hyperbolic Riemann surfaces.