Summary: A PLANCHEREL FORMULA ON Sp 4
Anne­Marie Aubert and Ju­Lee Kim
Abstract. In [HC], Harish­Chandra derived a Plancherel formula on p­adic groups. How­
ever, to have an explicit formula, one will have to compute the measures appearing in the
formula. Here, we compute the Plancherel measures on Sp 4 over p­adic fields explicitly.
Contents
Introduction
1. Harish­Chandra's Plancherel formula
1.1. Notation
1.2. fl(G=M), c(G=M) factors
1.3. ¯HC factors
1.4. The Plancherel formula d'apr`es Harish­Chandra
2. Transfer of the Plancherel measure
2.1. General results
2.2. The Plancherel measures on rank one groups
3. Sp 4 (k)
4. Construction of types and formal degrees of supercuspidal repre­
sentations
4.1. Summary of the construction of types
4.2. Computing formal degrees

Source: Aubert, Anne-Marie - Institut de Mathématiques de Jussieu

Collections: Mathematics