Hello, this is a question regarding Reineke's paper "Cohomology of non-commutative Hilbert schemes", http://arxiv.org/abs/math/0306185, and more precisely the formula on page 4 there (at $n=1$), namely: $$\chi(H_{d,1}^{(m)})=\frac{1}{(m-1)d+1}\binom{md}{d}$$

Here at left we have the cohomological Euler characteristic of the non-commutative Hilbert scheme $H_{d,1}^{(m)}$, and at right we have the Fuss-Catalan numbers.

The point now is that the Fuss-Catalan numbers appear as well in a key place in subfactor theory, namely as coefficients of the Poincaré series of the Fuss-Catalan algebra of Bisch and Jones (for a quick introduction to this algebra, see e.g. Bisch's survey paper http://arxiv.org/abs/math/0304340).

- Question: is there any serious relation between Reineke's formula and the Bisch-Jones formula?

(Note: regarding my own motivation, some 10 years ago I happened to attend a talk by Reineke, and, as a subfactor aficionado, when I saw that numbers on the blackboard I jumped on my seat! I asked him after his talk, he didn't know, and then for some time I kept asking people around, either in AG or in subfactors. But, so far, couldn't find anyone knowing well enough both subjects, in order to answer.)

noanswer would beautomaticallyaccepted. (The answer needs two votes!) The bounty would just expire (points still lost). – quid Feb 4 '13 at 17:40