You can write a[[1,2], [2,1]] in Julia, but it means something different from what it (apparently) means in numpy. The meaning in Julia is equivalent to the Matlab meaning.
To achieve what you seem to want you can use sub2ind:
*julia> **a[sub2ind(size(a), [1,2], [2,1])]*
*2-element Array{Int64,1}:*
* 2*
* 3*
