# M(3,1,1)

M(3,1,1) - $kC_3$
Representative: $kC_3$ $C_3$ $1$ 3 1 1 $k:k^*$ $\left( \begin{array}{c} 3 \\ \end{array} \right)$ Yes Yes Yes $\mathcal{O} C_3$ $\left( \begin{array}{c} 1 \\ 1 \\ 1 \\ \end{array}\right)$ 1 $\mathcal{L}(B)=S_3$ {{{PIgroup}}} Yes $kC_3$ Yes M(3,1,2) Yes M(3,1,2) {{{pcoveringblocks}}}

## Basic algebra

Quiver: a : <1,1>

Relations w.r.t. $k$: a^3=0

## Covering blocks and covered blocks

Let $N \triangleleft G$ with $p'$-index and let $B$ be a block of $\mathcal{O} G$ covering a block $b$ of $\mathcal{O} N$.

If $b$ lies in M(3,1,1), then $B$ must lie in M(3,1,1) or M(3,1,2). For example consider the principal blocks of $C_3 \triangleleft S_3$.

If $B$ lies in M(3,1,1), then $b$ must lie in M(3,1,1) or M(3,1,2). Example needed.