Abstract
AbstractLet be a (not necessarily simply laced) finite-dimensional complex simple Lie algebra with the Cartan subalgebra and Q ⊂ * the root lattice. Denote by ΘQ(q) the theta series of the root lattice Q of . We prove a curious “combinatorial” identity for the derivative of ΘQ(q), i.e. for by using the representation theory of an affine Lie algebra.
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