Jürgen Fuchs, Ingo Runkel, Christoph Schweigert
A Reason for Fusion Rules to be Even
Preprint series: ESI preprints

MSC:

18D10 Monoidal categories (= multiplicative categories), See also {19D23}

17B10 Representations, algebraic theory (weights)

20C05 Group rings of finite groups and their modules, See Also {

Abstract: We show that certain tensor product multiplicities in semisimple braided
sovereign tensor categories must be even. The quantity governing this
behavior is the Frobe\-ni\-us\hy Schur indicator. The result applies in
particular to the representation categories of large classes of groups,
Lie algebras, Hopf algebras and vertex algebras.

Keywords: Fusion rules, tensor product multiplicities, Frobenius-Schur indicator, sovereign tensor categories