Miniscule representations , Gauss sum and modular invariance 1
نویسنده
چکیده
After explaining the concepts of Langlands dual and miniscule representations, we define an analog of the Gauss sum for any compact, simple Lie group with a simply laced Lie algebra. We then show a reciprocity property when a Lie group is exchanged with its Langlands dual. We also explore the relation with theta functions and modular transformations. In the non-simply laced case, we construct a unitary representation of the Hecke group which involves interesting new phase factors. 2000 Mathematics Subject Classification: 22E46, 11F03, 11L03.
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