This morning I just discovered these corrigendathese corrigenda of K. Iohara and Y. Koga (in which my name is cited in acknowledgement). In fact, three years ago, I have contacted K. Iohara (author, with Y. Koga, of the book Representation Theory of the Virasoro Algebra) about this error (but I didn't know they fixed it).
I do not yet read these corrigenda into details, but I guess it's ok (I hope).
Another unfixed error for the Ramond algebra :
As I said in remark, F. Sauvageot gave a proof 'à la Langlands' of the FQS criterion for the superVirasoro algebras ($N=1$): the Neveu-Schwarz algebra and the Ramond algebra.
Seven years ago, during my PhD, I have discovered this error in this paper of Langlands, reproduced in this paper of Sauvageot, so I decided to write a proof "à la FQS" of the FQS criterion for the Neveu-Schwarz and Ramond algebras.
In fact I discovered that this criterion runs for the Neveu-Schwarz case,
but not for the Ramond case :
We can prove lemma 4.19 p 22 of this paperthis paper (Neveu-Schwarz case)
thanks to the curves $h=h^{m}_{pp}$, but the Ramond case doesn't have these curves !
So it's ok for the Neveu-Schwarz case (and I guess Sauvageot's paper is fixable in this case by using the corrigenda above), but for the Ramond case,
the FQS criterion gives the discrete series plus some representations of
charge $c_{m}$ with $m$ non-interger !
Sketch of fixing :
For excluding these last representations we can use an argument of
fusion:
$$ (R) \boxtimes (R) \to (NS) $$
It's known that the fusion of two representations of the Ramond algebra (R), in the discrete series at central charge $c_{m}$, give a (discrete series) representation of the Neveu-Schwarz algebra (NS) at the same central charge $c_{m}$ (the Ramond algebra is given by a twisted vertex module over the vertex operator algebra of the Neveu-Schwarz algebra). But we know that the Neveu-Schwarz case doesn't contain such representations at central charge $c_{m}$ with $m$ non-interger, the result follows.
