# M(16,14,12)

M(16,14,12) - $B_0(k(SL_2(16)))$
[[File: |250px]]
Representative: $B_0(k(SL_2(16)))$ $(C_2)^4$ $C_{15}$ 16 15 1 See below Yes Yes Yes $B_0(\mathcal{O}(SL_2(16)))$ See below 1 $C_4$ No Yes M(16,14,11) Yes

## 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 $b$ is in M(16,14,12), then $B$ is also in M(16,14,12).

## Irreducible characters

All irreducible characters have height zero.

## Cartan matrix

$\left( \begin{array}{ccccccc} 16 & 8 & 8 & 8 & 8 & 4 & 4 & 4 & 4 & 4 & 4 & 2 & 2 & 2 & 2 \\ 8 & 8 & 4 & 4 & 4 & 2 & 4 & 2 & 2 & 4 & 0 & 2 & 0 & 0 & 1 \\ 8 & 4 & 8 & 4 & 4 & 4 & 2 & 0 & 2 & 2 & 4 & 1 & 2 & 0 & 0 \\ 8 & 4 & 4 & 8 & 4 & 2 & 4 & 4 & 0 & 2 & 2 & 0 & 1 & 2 & 0 \\ 8 & 4 & 4 & 4 & 8 & 4 & 2 & 2 & 4 & 0 & 2 & 0 & 0 & 1 & 2 \\ 4 & 2 & 4 & 2 & 4 & 4 & 1 & 0 & 2 & 0 & 2 & 0 & 0 & 0 & 0 \\ 4 & 4 & 2 & 4 & 2 & 1 & 4 & 2 & 0 & 2 & 0 & 0 & 0 & 0 & 0 \\ 4 & 2 & 0 & 4 & 2 & 0 & 2 & 4 & 0 & 1 & 0 & 0 & 0 & 2 & 0 \\ 4 & 2 & 2 & 0 & 4 & 2 & 0 & 0 & 4 & 0 & 1 & 0 & 0 & 0 & 2 \\ 4 & 4 & 2 & 2 & 0 & 0 & 2 & 1 & 0 & 4 & 0 & 2 & 0 & 0 & 0 \\ 4 & 0 & 4 & 2 & 2 & 2 & 0 & 0 & 1 & 0 & 4 & 0 & 2 & 0 & 0 \\ 2 & 2 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 0 & 2 & 0 & 0 & 0 \\ 2 & 0 & 2 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 0 & 2 & 0 & 0 \\ 2 & 0 & 0 & 2 & 1 & 0 & 0 & 2 & 0 & 0 & 0 & 0 & 0 & 2 & 0 \\ 2 & 1 & 0 & 0 & 2 & 0 & 0 & 0 & 2 & 0 & 0 & 0 & 0 & 0 & 2 \end{array}\right)$

## Decomposition matrix

$\left( \begin{array}{ccccccc} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ 1 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 \\ 1 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 \\ 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \end{array}\right)$