Abstract
We construct local and global metaplectic double covers of odd general spin groups, using the cover of Matsumoto of spin groups. Following Kazhdan and Patterson, a local exceptional representation is the unique irreducible quotient of a principal series representation, induced from a certain exceptional character. The global exceptional representation is obtained as the multi-residue of an Eisenstein series: it is an automorphic representation, and it decomposes as the restricted tensor product of local exceptional representations. As in the case of the small representation of SO2n+1 of Bump, Friedberg, and Ginzburg, exceptional representations enjoy the vanishing of a large class of twisted Jacquet modules (locally), or Fourier coefficients (globally). Consequently they are useful in many settings, including lifting problems and Rankin-Selberg integrals. We describe one application, to a calculation of a co-period integral.
Original language | English |
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Pages (from-to) | 609-671 |
Number of pages | 63 |
Journal | Journal of the Institute of Mathematics of Jussieu |
Volume | 16 |
Issue number | 3 |
DOIs | |
State | Published - 1 Jun 2017 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© Cambridge University Press 2015.
Keywords
- GSpin groups
- co-period integral
- metaplectic cover
- small representations