Two extremely naive questions about the Kronecker problem from Geometric Complexity Theory
A) The input here is the triple of partitions $(\lambda, \mu, \nu)$, represented as sequences of numbers in binary. The dimension of the irreducible representation $M_{\lambda}$ can actually be exponential in $r$, take for example the hook partition $n + 1, 1, 1, \dots, 1 \vdash 2n + 1$. Using the hook formula for the dimension we get $\frac {(2n)!}{(n !)^2}$.

B) The $P$ in $\# P$ means polynomial time, but the $\#$ in $\#P$ means "count computation paths of a nondeterministic machine". An example of $\#P$ problem is $\#SAT$ (count the number of satisfying assignments for a given formula), and the corresponding decision problem is $SAT$, which is probably not in $P$.