Generic Transfer for General Spin Groups

By M. Asgari, F. Shahidi. 2004

113 citations recorded by the source corpus.

We prove Langlands functoriality for the generic spectrum of general spin groups (both odd and even). Contrary to other recent instances of functoriality, our resulting automorphic representations on the general linear group are not self-dual. Together with cases of classical groups, this completes the list of cases of split reductive groups whose L-groups have classical derived groups. The important transfer from GSp4 to GL4 follows from our result as a special case.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4cc293dded397bbb25d6cee0474f95d40d88acc3

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In Geometry and Topology

1. A. Raghuram
2. F. Shahidi
3. Shuichiro Takeda
4. W. Gan
5. H. Grobner
6. J. Cogdell
7. M. Asgari
8. Dinakar Ramakrishnan

In Mathematical Physics

1. F. Shahidi
2. A. Raghuram
3. Shuichiro Takeda
4. W. Gan
5. J. Cogdell
6. H. Grobner
7. M. Asgari
8. Dinakar Ramakrishnan

Citations in the corpus

• Functoriality for the quasisplit classical groups (2011, methodology): “Similar methods should work for the quasisplit GSpin groups, and this will be pursued by Asgari and Shahidi as a sequel to [5].”
• Generic transfer from GSp(4) to GL(4) (2004, methodology): “One is to prove an analogue of descent theory for these groups as was done for classical groups by Ginzburg, Rallis and Soudry [GRS01, Sou05].”
• SIEGEL MODULAR FORMS OF GENUS 2 ATTACHED TO ELLIPTIC CURVES (2006, background): “Asgari [4] to transfer Π back to a cuspidal automorphic representation π′ of GL(4,A), and by construction, π and π′ will have the same exterior square L-function.”
• The twisted symmetric square L -function of GL(r) (2010, methodology): “is paper will be used in a work by Asgari and Shahidi ([AS2]) for determination of the image of the Langlands transfers from the general spin groups to GLr which they obtained in their earlier paper ([AS1]). Notations Throughout the paper, Fwill be either a local or global field of characteristic 0. ”
• On the arithmetic of Shalika models and the critical values of L-functions for GL2n (2011, background): “One may also phrase the statement of the proposition in a motivic language: The representation Π conjecturally corresponds to a motive M , and via the L-factors at infinity one can write down the Hodge-pairs for M , i.e., pairs of integers (p, q) such that the Hodge number hp,q(M) 6= 0.”