This paper addresses the decomposition number problem for spin representations of symmetric groups in odd characteristic. Our main aim is to find a combinatorial formula for decomposition numbers in blocks of defect
2
2
, analogous to Richards’s formula for defect
2
2
blocks of symmetric groups.
By developing a suitable analogue of the combinatorics used by Richards, we find a formula for the corresponding “
q
q
-decomposition numbers”, i.e. the canonical basis coefficients in the level-
1
1
q
q
-deformed Fock space of type
A
2
n
(
2
)
A^{(2)}_{2n}
; a special case of a conjecture of Leclerc and Thibon asserts that these coefficients yield the spin decomposition numbers in characteristic
2
n
+
1
2n+1
. Along the way, we prove some general results on
q
q
-decomposition numbers. This paper represents the first substantial progress on canonical bases in type
A
2
n
(
2
)
A^{(2)}_{2n}
.