Mostrando recursos 1 - 11 de 11

  1. Free and non-free multiplicity on the arrangement of type$A_3-1$

    Abe, Takuro
    We give the first complete classification of free and non-free multiplicities on an arrangement, called the arrangement of type $A_3-1$, which admits both of them.

  2. Garsia-Haiman modules for hook partitions and Green polynomials with two variables

    Morita, Hideaki
    We consider Garsia-Haiman modules for the symmetric groups, a doubly graded generalization of Springer modules. Our main interest lies in singly graded submodules of a Garsia-Haiman module. We show that these submodules satisfy a certain combinatorial property, and verify that this property is implied by a behavior of Macdonald polynomials at roots of unity.

  3. Faces of arrangements of hyperplanes and Arrow's impossibility theorem

    Abe, Takuro
    In \cite{T}, Terao introduced an admissible map of chambers of a real central arrangement, and completely classified it. An admissible map is a generalization of a social welfare function and Terao's classification is that of Arrow's impossibility theorem in economics. In this article we consider an admissible map not of chambers but faces, and show that an admissible map of faces is a projection to a component if an arrangement is indecomposable and its cardinality is not less than three. From the view point of Arrow's theorem, our result corresponds to the impossibility theorem of a welfare function which permits the...

  4. シューア多項式の一般化におけるピエリルール

    Numata, Yasuhide

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

    Morita, Hideaki; Wachi, Akihito; Watanabe, Junzo

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 組み合わせ数学と対称性

    田辺, 顕一朗

  11. Remark on the weight enumerators and Siegel modular forms

    Choie, YoungJu; Oura, Manabu

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