Genuine Representations of the Metaplectic Group and Epsilon Factors

1995 ◽  
pp. 721-731 ◽  
Author(s):  
Jeffrey Adams
Keyword(s):  
Metaplectic Group ◽  
Epsilon Factors

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.

scholarly journals Endoscopie et conjecture locale raffinée de Gan–Gross–Prasad pour les groupes unitaires

2015 ◽  
Vol 151 (7) ◽  
pp. 1309-1371 ◽  
Author(s):  
R. Beuzart-Plessis
Keyword(s):  
Unitary Groups ◽  
Branching Laws ◽  
Epsilon Factors

Under endoscopic assumptions about $L$-packets of unitary groups, we prove the local Gan–Gross–Prasad conjecture for tempered representations of unitary groups over $p$-adic fields. Roughly, this conjecture says that branching laws for $U(n-1)\subset U(n)$ can be computed using epsilon factors.

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.

scholarly journals Product formula for p -adic epsilon factors

2014 ◽  
Vol 14 (2) ◽  
pp. 275-377 ◽  
Author(s):  
Tomoyuki Abe ◽  
Adriano Marmora
Keyword(s):  
Finite Field ◽  
Stationary Phase ◽  
Product Formula ◽  
Formula One ◽  
Etale Cohomology ◽  
Rigid Cohomology ◽  
Étale Cohomology ◽  
Analogous Formula ◽  
Epsilon Factors

AbstractLet $X$ be a smooth proper curve over a finite field of characteristic $p$. We prove a product formula for $p$-adic epsilon factors of arithmetic $\mathscr{D}$-modules on $X$. In particular we deduce the analogous formula for overconvergent $F$-isocrystals, which was conjectured previously. The $p$-adic product formula is a counterpart in rigid cohomology of the Deligne–Laumon formula for epsilon factors in $\ell$-adic étale cohomology (for $\ell \neq p$). One of the main tools in the proof of this $p$-adic formula is a theorem of regular stationary phase for arithmetic $\mathscr{D}$-modules that we prove by microlocal techniques.

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