A non-recursive criterion for weights of a highest-weight module for an affine Lie algebra (Q375774)

Let \(\mathfrak{g}\) be an affine Lie algebra and \(\Lambda\) a dominant integral weight of level \(k\). In this paper the authors study the support (i.e. the set of weights) of the simple highest weight \(\mathfrak{g}\)-module with highest weight \(\Lambda\). They propose a non-recursive criterion to determine whether some weight \(\eta\) belongs to this support. The criterion is given in terms of the coefficients of the weight \(\Lambda-\eta\) modulo a certain integral lattice (which depends on \(k\) but not on \(\eta\)) and requires computation of a certain set of the size comparable to the fundamental region of this lattice. It is shown that this set can be efficiently computed.