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Let $V$ be a $2g$-dimensional vector space over $\mathbb{Z}_3 := \mathbb{Z}/3\mathbb{Z}$. First, $\operatorname{Sp}(2g,\mathbb{Z}_3)$ acts on $\Lambda^2(V)$, and this decomposition is reducible, as ...

How to deduce the Loewy Structure of $kS_4$ where $k$ has characteristic 2. I can compute the Cartan matrix and Decomposition matrix with Brauer Characters without difficulties. But when it comes to ...

Suppose $G$ is a the cyclic group of $n$ elements and $p$ is a prime not in $n$. $G$ has an action on the cyclotomic field as a $\mathbb{Q}$-vector space $\mathbb{Q}[X] / \langle \Phi_n(X) \rangle$ by ...