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Volume 51 (1999)
- Issue 4 Pages 781-
- Issue 3 Pages 523-
- Issue 2 Pages 253-
- Issue 1 Pages 1-
Predecessor
- Proceedings of the Physico-Mathematical Society of Japan. 3rd Series
- Proceedings of the Tokyo Mathematico-Physical Society. 2nd Series
- Tokyo Sugaku-Butsurigakukwai Kiji-Gaiyo
- Tokyo Sugaku-Butsurigakkwai Hokoku
- Tokyo Sugaku-Butsurigaku Kwai Kiji
- Tokyo Sugaku-Butsurigaku Kwai Kiji
- Tokyo Sugaku Kaisya Zasshi
Volume 51, Issue 1
Displaying 1-13 of 13 articles from this issue
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Akihiko GYOJA, Kyo NISHIYAMA, Hiroyuki SHIMURA1999 Volume 51 Issue 1 Pages 1-34
Published: 1999
Released on J-STAGE: January 19, 2007
JOURNAL FREE ACCESSThe notion of two-sided cell, which was originally introduced by A. Joseph and reformulated by D. Kazhdan and G. Lusztig, has played an important role in the representation theory. Results concerning them have been obtained by very deep and sometimes ad hoc arguments. Here we introduce certain polynomial invariants for irreducible representations of Weyl groups. Our invariants are easily calculated, and the calculational results show that they almost determine the two-sided cells. Moreover, the factorization pattern of our polynomial invariants seems to be controlled by the natural parameter set \mathscr{M}(\mathscr{G}) of each two-sided cell.View full abstractDownload PDF (254K) -
Hiroyasu TSUCHIHASHI1999 Volume 51 Issue 1 Pages 35-44
Published: 1999
Released on J-STAGE: January 19, 2007
JOURNAL FREE ACCESSWe give a necessary condition for Galois covering singularities to be log-terminal or log-canonical singularities, which is also sufficient under a certain restriction on the branch loci of the covering maps. We also give a method constructing explicitly resolutions of 2-dimensional Abel covering singularities.View full abstractDownload PDF (146K) -
Kenshi ISHIGURO, Jesper MØLLER, Dietrich NOTBOHM1999 Volume 51 Issue 1 Pages 45-61
Published: 1999
Released on J-STAGE: January 19, 2007
JOURNAL FREE ACCESSFor G=S3וs× S3, let X be a space such that the p-completion (X)p^ is homotopy equivalent to (BG)p^ for any prime p. We investigate the monoid of rational equivalences of X, denoted by ε0(X). This topological question is transformed into a matrix problem over Qotimes Z^, since ε0(BG) is the set of monomial matrices whose nonzero entries are odd squares. It will be shown that a submonoid of ε0(X), denoted by δ0(X), determines the decomposability of X. Namely, if Nodd denotes the monoid of odd natural numbers, Theorem 2 shows that the monoid δ0(X) is isomorphic to a direct sum of copies of Nodd. Moreover the space X splits into m indecomposable spaces if and only if δ0(X)_??_(Nodd)m. When such a space X is indecomposable, the relationship between [X, X] and [BG, BG] is discussed. Our results indicate that the homotopy set [X, X] contains less maps if X is not homotopy equivalent to the product of quaternionic projective spaces BG=HP∈ftyוs× HP∈fty.View full abstractDownload PDF (166K) -
András NÉMETHI1999 Volume 51 Issue 1 Pages 63-70
Published: 1999
Released on J-STAGE: January 19, 2007
JOURNAL FREE ACCESSIf a polynomial map f:Cn→ C has a nice behaviour at infinity (e.g. it is a“good polynomial”), then the Milnor fibration at infinity exists, in particular, one can define the Seifert form at infinity Γ(f) associated with f. In this paper we prove a Sebastiani-Thom type formula. Namely, if f:Cn→ C and g:Cm→ C are“good”polynomials, and we define h=f+g:Cn+m→ C by h(x, y)=f(x)+g(y), then Γ(h)=(-1)mnΓ(f) Γ(g). This is the global analogue of the local result, proved independently by K. Sakamoto and P. Deligne for isolated hypersurface singularities.View full abstractDownload PDF (113K) -
Mamoru MIMURA, Hideaki OSHIMA1999 Volume 51 Issue 1 Pages 71-92
Published: 1999
Released on J-STAGE: January 19, 2007
JOURNAL FREE ACCESSWe prove that if X is a connected H-space with at most three cells of positive dimension, then the self homotopy set of X becomes a group relative to the binary operation induced from any multiplication on X, and we determine it's group structure in some cases.View full abstractDownload PDF (206K) -
Yoshikazu HIRAI1999 Volume 51 Issue 1 Pages 93-128
Published: 1999
Released on J-STAGE: January 19, 2007
JOURNAL FREE ACCESSIn this paper we give an explicit Fourier expansion of the Eisenstein series on certain quaternion unitary groups of degree 2 by means of Shimura's method. Moreover using an explicit formula of the Fourier coefficients of holomorphic Eisenstein series and Oda's lifted cusp forms, we give some numerical examples.View full abstractDownload PDF (263K) -
Dedicated to Professor Takeshi Hirai on his sixtieth birthdayAkihiko GYOJA, Hiroshi YAMASHITA1999 Volume 51 Issue 1 Pages 129-149
Published: 1999
Released on J-STAGE: January 19, 2007
JOURNAL FREE ACCESSLet \mathfrak{g} be a complex semisimple Lie algebra with symmetric decomposition \mathfrak{g}=\mathfrak{f}+\mathfrak{p}. For each irreducible Harish-Chandra (\mathfrak{g}, \mathfrak{f})-module X, we construct a family of nilpotent Lie subalgebras \mathfrak{n}(\mathcal{O}) of \mathfrak{g} whose universal enveloping algebras U(\mathfrak{n}(\mathcal{O})) act on X locally freely. The Lie subalgebras \mathfrak{n}(\mathcal{O}) are parametrized by the nilpotent orbits \mathcal{O} in the associated variety of X, and they are obtained by making use of the Cayley tranformation of \mathfrak{s}\mathfrak{l}2-triples (Kostant-Sekiguchi correspondence). As a consequence, it is shown that an irreducible Harish-Chandra module has the possible maximal Gelfand-Kirillov dimension if and only if it admits locally free U(\mathfrak{n}m)-action for \mathfrak{n}m=\mathfrak{n}(\mathcal{O}max) attached to a principal nilpotent orbit \mathcal{O}max in \mathfrak{p}$.View full abstractDownload PDF (189K) -
Dedicated to Professor Takashi Ono on his seventieth birthdayMing-Guang LEU1999 Volume 51 Issue 1 Pages 151-166
Published: 1999
Released on J-STAGE: January 19, 2007
JOURNAL FREE ACCESSIn this article, let k≡ 0 or 1 (mod 4) be a fundamental discriminant, and let Χ(n) be the real even primitive character modulo k. The series \[ L(1, Χ)=∑_{n=1}∞\frac{Χ(n)}{n} \] can be divided into groups of k consecutive terms. Let v be any nonnegative integer, j an integer, 0≤ j≤ k-1, and let \[T(v, j, Χ)=∑_{n=j+1}j+k\frac{Χ(vk+n)}{vk+n} \] Then L(1, \displaystyle Χ)=∑_{v=0}∞T(v, 0, Χ)=∑_{n=1}jΧ(n)/n+∑_{v=0}∞T(v, j, Χ).
In section 2, Theorems 2.1 and 2.2 reveal a surprising relation between incomplete character sums and partial sums of Dirichlet series. For example, we will prove that T(v, j, Χ)• M<0 for integer v\displaystyle ≥qmax{1, √{k}/|M|} if M=\displaystyle ∑_{m=1}j-1Χ(m)+1/2Χ(j)≠ 0 and |M|≥q 3/2. In section 3, we will derive algorithm and formula for calculating the class number of a real quadratic field. In section 4, we will attempt to make a connection between two conjectures on real quadratic fields and the sign of T(0, 20, Χ)$.View full abstractDownload PDF (130K) -
Takeyoshi SATO1999 Volume 51 Issue 1 Pages 167-179
Published: 1999
Released on J-STAGE: January 19, 2007
JOURNAL FREE ACCESSThe classical Fatou limit theorem was extended to the case of positive harmonic functions on a hyperbolic Riemann surface R by Constantinescu-Cornea. They used extensively the notions of Martin's boundary and fine limit following the filter generated by the base of the subsets of R whose complements are closed and thin at a minimal boundary point of R. We shall consider such a problem for positive solutions of the Schrödinger equation on a hyperbolic Riemann surface.View full abstractDownload PDF (112K) -
Dedicated to Professor Rentaro Agemi on the occasion of his sixtieth birthdayWakako DAN, Yoshihiro SHIBATA1999 Volume 51 Issue 1 Pages 181-207
Published: 1999
Released on J-STAGE: January 19, 2007
JOURNAL FREE ACCESSWe proved Lq-Lr type estimates of the Stokes semigroup in a two dimensional exterior domain. Our proof is based on the local energy decay estimate obtained by investigation of the asymptotic behavior of the resolvent of the Stokes operator near the origin.View full abstractDownload PDF (225K) -
Qing-Ming CHENG, Susumu ISHIKAWA, Katsuhiro SHIOHAMA1999 Volume 51 Issue 1 Pages 209-226
Published: 1999
Released on J-STAGE: January 19, 2007
JOURNAL FREE ACCESSWe classify complete conformally flat three dimensional Riemannian manifolds with constant scalar curvature and constant squared norm of Ricci curvature tensor by applying the Generalized Maximum Principle due to H. Omori.View full abstractDownload PDF (131K) -
Dedicated to Professor Hiroyasu Ishimoto on his 60th birthdayKazuhiko FUKUI, Hideki IMANISHI1999 Volume 51 Issue 1 Pages 227-236
Published: 1999
Released on J-STAGE: January 19, 2007
JOURNAL FREE ACCESSWe consider the group of foliation preserving homeomorphisms of a foliated manifold. We compute the first homologies of the groups for codimension one foliations. Especially, we show that the group for the Reeb foliation on the 3-sphere is perfect and the groups for irrational linear foliations on the torus are not perfect.View full abstractDownload PDF (118K) -
Fernando CHAMIZO1999 Volume 51 Issue 1 Pages 237-252
Published: 1999
Released on J-STAGE: January 19, 2007
JOURNAL FREE ACCESSWe prove an asymptotic formula for \displaystyle ∑n≤ Nr(n)r(n+m) using the spectral theory of automorphic forms and we specially study the uniformity of the error term in the asymptotic approximation when m varies. The best results are obtained under a natural conjecture about the size of a certain spectral mean of the Maass forms.
We also employ large sieve type inequalities for Fourier coefficients of cusp forms to estimate some averages (over m) of the error term.View full abstractDownload PDF (134K)
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