  The Hilbert space of level $q$ Chern-Simons theory of gauge group $G$ of the
ADE type quantized on $T^2$ can be represented by points that lie on the weight
lattice of the Lie algebra $\mathfrak{g}$ up to some discrete identifications.
Of special significance are the points that also lie on the root lattice. The
generating functions that count the number of such points are quasi-periodic
Ehrhart polynomials which coincide with the generating functions of $SU(q)$
representation of the ADE subgroups of $SU(2)$ given by the McKay
correspondence. This coincidence has roots in a string/M theory construction
where D3(M5)-branes are put along an ADE singularity. Finally, a new
perspective on the McKay correspondence that involves the inverse of the Cartan
matrices is proposed.
