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$GL(m|n)$-supermodules with good and Weyl filtrations (1406.3757v1)
Published 14 Jun 2014 in math.RA and math.RT
Abstract: The purpose of this paper is to prove necessary and sufficient criteria for a $GL(m|n)$-supermodule to have a good or Weryl filtration. We also introduce the notion of a Steinberg supermodule analogous to the classical notion of Steinberg module. We prove that the Steinberg supermodule inherits some properties of the Steinberg module. Some new series of finite-dimensional tilting supermodules are found.