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Noriyuki Abe

  1. First extension groups of Verma modules and $R$-polynomials.

    Втр, 03/02/2010 - 16:01 — SomNambul
    Authors: Noriyuki Abe
    Subjects: Representation Theory
    Abstract

    We study the first extension groups between Verma modules. There was a
    conjecture which claims that the dimensions of the higher extension groups
    between Verma modules are the coefficients of $R$-polynomials defined by
    Kazhdan-Lusztig. This conjecture was known as the Gabber-Joseph conjecture
    (although Gebber and Joseph did not state.) However, Boe gives a counterexample
    to this conjecture. In this paper, we study how far are the dimensions of
    extension groups from the coefficients of $R$-polynomials.

  2. General heart construction on a triangulated category (II): Associated cohomological functor.

    Пт, 10/16/2009 - 04:10 — SomNambul
    Authors: Hiroyuki Nakaoka, Noriyuki Abe
    Subjects: Category Theory
    Abstract

    In the preceding part (I) of this paper, we showed that for any torsion pair
    (i.e., $t$-structure without the shift-closedness) in a triangulated category,
    there is an associated abelian category, which we call the heart. Two extremal
    cases of torsion pairs are $t$-structures and cluster tilting subcategories. If
    the torsion pair comes from a $t$-structure, then its heart is nothing other
    than the heart of this $t$-structure. In this case, as is well known, by
    composing certain adjoint functors, we obtain a cohomological functor from the
    triangulated category to the heart.

Math-arch

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