Endoscopy and the transfer from \(\mathrm{GSp}(4)\) to \(\mathrm{GL}(4)\)
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Publication:487149
DOI10.1515/FORUM-2012-0006zbMATH Open1323.11029arXiv1011.6415OpenAlexW2964182778MaRDI QIDQ487149
Author name not available (Why is that?)
Publication date: 19 January 2015
Published in: (Search for Journal in Brave)
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 �oxplus 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).
Full work available at URL: https://arxiv.org/abs/1011.6415
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