[R-sig-ME] meaning of lmer formula

[Don Cohen]

My current understanding is that something like (input2 | group)
means the same as (1 + input2 | group) which means to estimate
for each group an intercept, a slope and a correlation between the two.

Does (input1 + input2 | group) mean the same as
(input1 | group) + (input2 | group) or does it also include a 
correlation between input1 and input2 ?

Back to my question about additive shifts, is that extra correlation 
required in order to maintain invariance over additive shifts?

Is there some way in the formula language to control more precisely
which correlations are to be included/excluded?