scholarly journals Admissibility for a class of subgroups of the metaplectic group

2019 ◽  
Author(s):  
Eckart Schulz ◽  
Kampanat Namgam
Keyword(s):  
Metaplectic Group

scholarly journals Siegel modular forms and theta series attached to quaternion algebras

1991 ◽  
Vol 121 ◽  
pp. 35-96 ◽  
Author(s):  
Siegfried Böcherer ◽  
Rainer Schulze-Pillot
Keyword(s):  
Modular Forms ◽  
Orthogonal Group ◽  
Automorphic Forms ◽  
Theta Series ◽  
Siegel Modular Forms ◽  
Theta Correspondence ◽  
Quaternion Algebras ◽  
Metaplectic Group

The two main problems in the theory of the theta correspondence or lifting (between automorphic forms on some adelic orthogonal group and on some adelic symplectic or metaplectic group) are the characterization of kernel and image of this correspondence. Both problems tend to be particularly difficult if the two groups are approximately the same size.

The metaplectic group within the Heisenberg–Weyl ring

1986 ◽  
Vol 27 (1) ◽  
pp. 29-36 ◽  
Author(s):  
Mauricio García‐Bullé ◽  
Wolfgang Lassner ◽  
Kurt Bernardo Wolf
Keyword(s):  
Metaplectic Group

Squeezed states, metaplectic group, and operator Möbius transformations

1994 ◽  
Vol 50 (1) ◽  
pp. 39-61 ◽  
Author(s):  
Arvind ◽  
Biswadeb Dutta ◽  
C. L. Mehta ◽  
N. Mukunda
Keyword(s):  
Squeezed States ◽  
Möbius Transformations ◽  
Metaplectic Group ◽  
Mobius Transformations

scholarly journals Geometric Weil representation: local field case

2009 ◽  
Vol 145 (1) ◽  
pp. 56-88 ◽  
Author(s):  
Vincent Lafforgue ◽  
Sergey Lysenko
Keyword(s):  
Local Field ◽  
Dual Pair ◽  
Weil Representation ◽  
Closed Field ◽  
Perverse Sheaves ◽  
Algebraically Closed Field ◽  
Field Case ◽  
Metaplectic Group ◽  
Geometric Langlands ◽  
Langlands Functoriality

AbstractLet k be an algebraically closed field of characteristic greater than 2, and let F=k((t)) and G=𝕊p2d. In this paper we propose a geometric analog of the Weil representation of the metaplectic group $\widetilde G(F)$. This is a category of certain perverse sheaves on some stack, on which $\widetilde G(F)$ acts by functors. This construction will be used by Lysenko (in [Geometric theta-lifting for the dual pair S𝕆2m, 𝕊p2n, math.RT/0701170] and subsequent publications) for the proof of the geometric Langlands functoriality for some dual reductive pairs.

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