Cohomology and Ext for blocks whose Brauer trees are lines or stars

Figures & data

Fig. 1 A star and a line.

Table 1 Character table for $\text{Sz}(q)$.

	1	x^a	y^b	z^c	t	f	$f^{-1}$
1	1	1	1	1	1	1	1
Π	q^2	1	−1	−1	0	0	0
${\Gamma }_1$	$\frac{s}{2}(q-1)$	0	1	–1	$-\frac{s}{2}$	$\frac{\mathit{\text{si}}}{2}$	$-\frac{\mathit{\text{si}}}{2}$
${\Gamma }_2$	$\frac{s}{2}(q-1)$	0	1	–1	$-\frac{s}{2}$	$-\frac{\mathit{\text{si}}}{2}$	$\frac{\mathit{\text{si}}}{2}$
Ωu	$q^2+1$	${\omega }^{\mathit{\text{ua}}}+{\omega }^{-\mathit{\text{ua}}}$	0	0	1	1	1
Θl	$(q-1)(q-s+1)$	0	$-{\epsilon }_{\mathit{\text{lb}}}$	0	s – 1	–1	–1
Λv	$(q-1)(q+s+1)$	0	0	$-{\delta }_{\mathit{\text{vc}}}$	$-s-1$	–1	–1