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Lifting of characters on p-adic orthogonal and metaplectic groups
- Part of
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- Journal:
- Compositio Mathematica / Volume 146 / Issue 3 / May 2010
- Published online by Cambridge University Press:
- 18 March 2010, pp. 795-810
- Print publication:
- May 2010
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- Article
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Let F be a p-adic field. Consider a dual pair
where SO(2n+1)+ is the split orthogonal group and 
is the metaplectic cover of the symplectic group Sp(2n) over F. We study lifting of characters between orthogonal and metaplectic groups. We say that a representation of SO(2n+1)+ lifts to a representation of 
if their characters on corresponding conjugacy classes are equal up to a transfer factor. We study properties of this transfer factor, which is essentially the character of the difference of the two halves of the oscillator representation. We show that the lifting commutes with parabolic induction. These results were motivated by the paper ‘Lifting of characters on orthogonal and metaplectic groups’ by Adams who considered the case F=ℝ.
where 
is the metaplectic cover of the symplectic group 
if their characters on corresponding conjugacy classes are equal up to a transfer factor. We study properties of this transfer factor, which is essentially the character of the difference of the two halves of the oscillator representation. We show that the lifting commutes with parabolic induction. These results were motivated by the paper ‘Lifting of characters on orthogonal and metaplectic groups’ by Adams who considered the case 