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Eric Sommers

  1. Exterior powers of the reflection representation in Springer theory.

    Пнд, 08/09/2010 - 15:01 — SomNambul
    Authors: Eric Sommers
    Subjects: Representation Theory
    Abstract

    We give a proof of a conjecture of Lehrer and Shoji regarding the occurrences
    of the exterior powers of the reflection representation in the cohomology of
    Springer fibers. The actual theorem proved is a slight extension of the
    original conjecture to all nilpotent orbits and also takes into account the
    action of the component group. The method is to use Shoji's approach to the
    orthogonality formulas for Green functions to relate the symmetric algebra to a
    sum over Green functions.

  2. Pieces of nilpotent cones for classical groups.

    Втр, 01/26/2010 - 16:01 — SomNambul
    Authors: Anthony Henderson, Pramod N. Achar, Eric Sommers
    Subjects: Representation Theory
    Abstract

    We compare orbits in the nilpotent cone of type $B_n$, that of type $C_n$,
    and Kato's exotic nilpotent cone. We prove that the number of $\F_q$-points in
    each nilpotent orbit of type $B_n$ or $C_n$ equals that in a corresponding
    union of orbits, called a type-$B$ or type-$C$ piece, in the exotic nilpotent
    cone. This is a finer version of Lusztig's result that corresponding special
    pieces in types $B_n$ and $C_n$ have the same number of $\F_q$-points. The
    proof requires studying the case of characteristic 2, where more direct
    connections between the three nilpotent cones can be established.

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