Miniscule representations, Gauss sum and modular invariance

Details Miniscule representations, Gauss sum and modular invariance Miniscule representations, Gauss sum and modular invariance

2008-02-14

arxiv.org/abs/0802.2038v1

Proc. of the 4th Intern. Congr. of Chinese Mathematicians, Vol.I, pp. 442-455 (2007)

Mathematics

Representation Theory

12 pages, corrected version

Scientific paper

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.

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