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Nicolas Ressayre

  1. Two generalizations of the PRV conjecture.

    Wed, 04/14/2010 - 15:01 — SomNambul
    Authors: Nicolas Ressayre, Pierre-Louis Montagard, Boris Pasquier
    Subjects: Representation Theory
    Abstract

    Let G be a complex connected reductive group. The PRV conjecture, which was
    proved independently by S. Kumar and O. Mathieu in 1989, gives explicit
    irreducible submodules of the tensor product of two irreducible G-modules. This
    paper has three aims. First, we simplify the proof of the PRV conjecture, then
    we generalize it to other branching problems. Finally, we find other
    irreducible components of the tensor product of two irreducible G-modules that
    appear for "the same reason" as the PRV ones.

  2. Branching Schubert calculus and the Belkale-Kumar product on cohomology.

    Mon, 09/07/2009 - 10:33 — SomNambul
    Authors: Nicolas Ressayre, Edward Richmond
    Subjects: Algebraic Geometry
    Abstract

    In 2006, Belkale and Kumar define a new product on the cohomology of flag
    varieties and use this new product to give an improved solution to the
    eigencone problem for complex reductive groups. In this paper, we give a
    generalization of the Belkale-Kumar product to the branching Schubert calculus
    setting. The study of Branching Schubert calculus attempts to understand the
    induced map on cohomology of an equivariant embedding of flag varieties. The
    main application of our work is a compact formulation of the solution to the
    branching eigencone problem.

  3. Branching Schubert calculus and the Belkale-Kumar product on cohomology.

    Mon, 09/07/2009 - 10:33 — SomNambul
    Authors: Nicolas Ressayre, Edward Richmond
    Subjects: Algebraic Geometry
    Abstract

    In 2006, Belkale and Kumar define a new product on the cohomology of flag
    varieties and use this new product to give an improved solution to the
    eigencone problem for complex reductive groups. In this paper, we give a
    generalization of the Belkale-Kumar product to the branching Schubert calculus
    setting. The study of Branching Schubert calculus attempts to understand the
    induced map on cohomology of an equivariant embedding of flag varieties. The
    main application of our work is a compact formulation of the solution to the
    branching eigencone problem.

  4. Spherical homogeneous spaces of minimal rank.

    Fri, 09/04/2009 - 12:10 — SomNambul
    Authors: Nicolas Ressayre
    Subjects: Algebraic Geometry
    Abstract

    Let $G$ be a complex connected reductive algebraic group and $G/B$ denote the
    flag variety of $G$. A $G$-homogeneous space $G/H$ is said to be {\it
    spherical} if $H$ acts on $G/B$ with finitely many orbits. A class of spherical
    homogeneous spaces containing the tori, the complete homogeneous spaces and the
    group $G$ (viewed as a $G\times G$-homogeneous space) has particularly nice
    proterties.

  5. A cohomology free description of eigencones in type A, B and C.

    Tue, 09/01/2009 - 12:47 — SomNambul
    Authors: Nicolas Ressayre
    Subjects: Algebraic Geometry
    Abstract

    Let $K$ be a connected compact Lie group. The triples $(O_1, O_2, O_3)$ of
    adjoint $K$-orbits such that $O_1+O_2+O_3$ contains 0 are parametrized by a
    closed convex polyhedral cone. This cone is denoted $\Gamma(K)$ and called the
    eigencone of $K$. For $K$ simple of type $A$, $B$ or $C$ we give an inductive
    cohomology free description of the minimal set of linear inequalities which
    characterizes $\Gamma(K)$.

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