Simon M. Goodwin

  1. Conjugacy classes in Sylow p-subgroups of finite Chevalley groups in bad characteristic.

    Authors: Simon M. Goodwin, John D. Bradley
    Subjects: Group Theory
    Abstract

    Let $U = \mathbf U(q)$ be a Sylow $p$-subgroup of a finite Chevalley group $G
    = \mathbf G(q)$. In [GR}] R\"ohrle and the second author determined a
    parameterization of the conjugacy classes of $U$, for $\mathbf G$ of small rank
    when $q$ is a power of a good prime for $\mathbf G$. As a consequence they
    verified that the number $k(U)$ of conjugacy classes of $U$ is given by a
    polynomial in $q$ with integer coefficients. In the present paper, we consider
    the case when $p$ is a bad prime for $\mathbf G$.

  2. Translation for finite W-algebras.

    Authors: Simon M. Goodwin
    Subjects: Representation Theory
    Abstract

    A finite $W$-algebra $U(\g,e)$ is a certain finitely generated algebra that
    can be viewed as the enveloping algebra of the Slodowy slice to the adjoint
    orbit of a nilpotent element $e$ of a complex reductive Lie algebra $\g$. It is
    possible to give the tensor product of a $U(\g,e)$-module with a finite
    dimensional $U(\g)$-module the structure of a $U(\g,e)$-module; we refer to
    such tensor products as translations.

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