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On some partition identities related to affine Lie algebra representations

In this paper, meant for combinatorialists, we give a proof of equipotence of two families of partitions (’Primc conjecture’) which appeared in the early stage of representation theory of affine Lie algebra A(1) 1 (or Sl(2, C)∧). The result was obtained already in 1983 and it lead to the very first character formulas for the level 3 standard modules (this is mentioned in Ref[1]) on pages 2 and 77 respectively). We hope that the intricacy of handling the interlocking recursion rela- tions may be of some interest to combinatorialists not working in Lie algebra theory.

partition function, partition identity, Lie algebra

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