Endoscopy and the Transfer from GSp(4) to GL(4)
Number Theory
2010-12-01 v1
Abstract
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).
Keywords
Cite
@article{arxiv.1011.6415,
title = {Endoscopy and the Transfer from GSp(4) to GL(4)},
author = {Bogume Jang},
journal= {arXiv preprint arXiv:1011.6415},
year = {2010}
}