Angular mometum of particles in FQHE hierarchy states

Question

I'm reading through David Tong's notes on the quantum hall effect, and I'm stuck understanding his argument for the filling fraction of hierarchy states. The relevant discussion is under A Quantum Hall Liquid of Quasi-Holes in section 3.3.1.

DT argues that the wavefunction for anyons with statistical parameter $\alpha = 1/m$ should be (ignoring the normalization constant): $$\Pi_{j<k}\left(\eta_j - \eta_k\right)^{2p+\alpha}e^{-\sum_{i}\left|\eta_{i}\right|^2/4l_B^2}$$

He then goes on to claim that

The maximum angular momentum of a given quasi-excitation is $N (2p \pm 1/m)$ where the $\pm$ sign is inherited from the charge of the quasi-excitation.

Question Why would a quasi-particle have a different maximum angular momentum than a quasi-hole? Expanding the polynomial in the front yields a monomial of degree $𝑁(2𝑝 +1/𝑚)$ in either case.

I've tried looking up references on hierarchy states in the FQHE but I can't find anything which reproduces this counting argument.

TIA.

Answer 1

There appears to be a number of typos in that section unfortunately. The correct expression should be $\alpha = \pm 1/m$. The corrected formulae are used in the corresponding online lectures.