Mostrando recursos 1 - 14 de 14

  1. 対数的ベクトル場のなす加群の基底を求めるアルゴリズム

    Numata, Yasuhide
    2 次元ベクトル空間上の原点を通る超平面(直線) の有限集合を考え, 各超平面に非負整数の重みをつけたものを2-multiarrangement と呼ぶ. 2-multiarrangementに対し, 対数的ベクトル場と呼ばれるベクトル場たちのなす加群を対応させる. 2次元ベクトル空間上で考えるとき, その加群は, 重みつき超平面配置の取り方によらず自由であり, その基底は斉次に取れることが知られている. 本稿では, 基底を帰納的に構成するアルゴリズムを与える.

  2. Linearity Defects of Face Rings

    Okazaki, Ryota

  3. ヒルベルト関数を固定した時の斉次イデアルのdepthについて

    Murai, Satoshi


    Miyahara, Hiroaki; Nishida, Kenji
    We study Gorenstein dimension and grade of a module M over a ltered ring whose assosiated graded ring is a commutative Noetherian ring. An equality or an inequality between these invariants of a ltered module and its associated graded module is the most valuable property for an investigation of ltered rings. We prove an inequality G-dimM G-dim grM and an equality gradeM = grade grM, whenever Gorenstein dimension of grM is nite (Theorems 2.3 and 2.8). We would say that the use of G-dimension adds a new viewpoint for studying ltered rings and modules. We apply these results to a ltered ring with a Cohen-Macaulay or Gorenstein...

  5. Zero-dimensional Gorenstein algebras with the action of the symmetric group S^k

    Morita, Hideaki; Wachi, Akihito; Watanabe, Junzo

  6. On elliptic cyclopean forms

    Miyake, Toshitsune; Maeda, Yoshitaka

  7. On integral formulas for convex domains

    Cielak, Waldemar; Koshi, Shozo; Zajac, Jozef

  8. Green polynomials at roots of unity and its application

    Morita, Hideaki
    We consider Green polynomials at roots of unity. We obtain a recursive formula for Green polynomials at appropriate roots of unity, which is described in a combinatorial manner. The coefficients of the recursive formula are realized by the number of permutations satisfying a certain condition, which leads to interpretation of a combinatorial property of certain graded modules of the symmetric group in terms of representation theory.

  9. A formula of Lascoux-Leclerc-Thibon and representations of symmetric groups

    Morita, Hideaki; Nakajima, Tatsuhiro
    We consider Green polynomials at roots of unity, corresponding to partitions which we call $l$-partitions. We obtain a combinatorial formula for Green polynomials corresponding to $l$-partitions at primitive $l$-th roots of unity. The formula is rephrased in terms of representation theory of the symmetric group.

  10. Zero dimensional Gorenstein algebras with the action of the symmetric group $S_k$

    Morita, Hideaki; Watanabe, Junzo
    We consider irreducible decompositions of certain Artinian algebras with the action of the symmetric group. The equi-degree monomial complete intersection can be thought of as a k-fold tensor of an n dimensional vector space. Otherwise put the tensor space can be given a commutative ring structure. From this view point we show that, in the case n=2 or k=2, the strong Lefschetz property can be used efficiently to decompose the algebra into irreducible components. We apply the result to determin a minimal generating set of certain Gorenstein ideal. Also we show that the Hilbert function of certain ring of invariants is a q-anolog of the binomial coefficent.

  11. Decomposition of Green polynomials of type $A$ and DeConcini-Procesi-Tanisaki algebras of certain types

    Morita, Hideaki
    A class of graded representations of the symmetric group, concerning with the cohomology ring of the corresponding flag variety, are considered. We point out a certain combinatorial property of the Poincar\'e polynomial of these graded representations, and interpret it in the language of representation theory of the symmetric group.

  12. On semisimple extensions of serial rings

    Hirata, K; Sugano, K

  13. Associated variety, Kostant$B!>(BSekiguchi correspondence, and locally free U(n)$B!>(Baction on Harish$B!>(BChandra modules

    Gyoja, A; Yamashita, H

  14. On bicommutators of modules over H‐separable extension rings III

    Sugano, Kozo

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