Abstract
We describe the algebra of matrices commuting with the action of the modular group on characters ofSU(N) k integrable representations. Using methods of finite quantum mechanics we find a canonical basis for this commutant over ℂ and prove the existence of an equivalent basis over ℚ with integral matrix elements. A final section is devoted to the case ofSU(3).
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Communicated by K. Gawedzki
Laboratoire de l'Institut de Recherche Fondamentale du Commissariat à l'Energie Atomique
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Bauer, M., Itzykson, C. Modular transformations ofSU(N) affine characters and their commutant. Commun.Math. Phys. 127, 617–636 (1990). https://doi.org/10.1007/BF02104506
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DOI: https://doi.org/10.1007/BF02104506