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For the Klein-Four Group $G$ and a perfect field $k$ of characteristic two we determine all indecomposable symplectic $kG$-modules, that is, $kG$-modules with a symplectic, $G$-invariant form which do not decompose into smaller such modules, and classify them up to isometry. Also we determine all quadratic forms that have one of the above symplectic forms as their associated bilinear form and describe their isometry classes.
Let $P$ be a principal indecomposable module of a finite group $G$ in characteristic $2$ and let $varphi$ be the Brauer character of the corresponding simple $G$-module. We show that $P$ affords a non-degenerate $G$-invariant quadratic form if and on
We determine the quadratic type of the 2-modular principal indecomposable modules of the double covers of alternating groups.
Let $alpha$ be a composition of $n$ and $sigma$ a permutation in $mathfrak{S}_{ell(alpha)}$. This paper concerns the projective covers of $H_n(0)$-modules $mathcal{V}_alpha$, $X_alpha$ and $mathbf{S}^sigma_{alpha}$, which categorify the dual immacula
In this paper, we study the tensor structure of category of finite dimensional representations of Drinfeld quantum doubles $D(H_n(q))$ of Taft Hopf algebras $H_n(q)$. Tensor product decomposition rules for all finite dimensional indecomposable modules are explicitly given.
We examine in detail the Jacobi-Trudi characters over the ortho-symplectic Lie superalgebras spo(2|2m+1) and spo(2n|3). We furthermore relate them to Serganovas notion of Euler characters.