Character formula and Plancherel formula for solvable almost connected Lie groups over a \(p\)-adic field (Q656205)
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scientific article; zbMATH DE number 5998260
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Character formula and Plancherel formula for solvable almost connected Lie groups over a \(p\)-adic field |
scientific article; zbMATH DE number 5998260 |
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Character formula and Plancherel formula for solvable almost connected Lie groups over a \(p\)-adic field (English)
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17 January 2012
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Following Duflo--Vergne (for real reductive groups) and Khalgui--Torasso (for real almost algebraic groups), the author proves the Plancherel formula for almost connected solvable \(p\)-adic groups (\(p\neq 2\)). To do this, a necessary and sufficient condition for a unitary irreducible representation to be admissible in terms of the Kirillov--Duflo orbit method is given. Then a character formula around each semi-simple element is established.
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