Endoscopy and the Transfer from GSp(4) to GL(4)

Details Endoscopy and the Transfer from GSp(4) to GL(4) Endoscopy and the Transfer from GSp(4) to GL(4)

2010-11-29

arxiv.org/abs/1011.6415v1

Mathematics

Number Theory

Scientific paper

We show the existence of an L-functions of a cuspidal representation of GSp(4,A)*GSp(4,A) which has a pole of order 2 at s = 1, even for globally generic representations. However if \pi comes from GSO(4,A), then \pi? is the Weil transfer of \Pi_?1 \otimes \Pi_2 realized as a representation of GSO(4,A). This agrees with Langlands Functoriality principle as GSO(4) is an endoscopic group for GSp(4) and shows that data ?\Pi_?1 \otimes \Pi_2 on GSO(4) transfers to \Pi_?1 \boxplus \Pi_2 through the composite of the endoscopic transfer from GSO(4) to GSp(4) and the twisted endoscopic transfer from GSp(4) to GL(4).

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