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Mackey inner product for the finite SL2 principal series

For one-dimensional representations

θ, φ

of the upper-triangular subgroup

B \leq S L_{2} (F_{p})

,

⟨ Ind_{B}^{G} θ, Ind_{B}^{G} φ ⟩_{G} = 1_{θ = φ} + 1_{θ^{w} ∣_{T} = φ ∣_{T}},

where

θ^{w} (t) = θ (w^{- 1} tw)

.

Table of contents 53 1
- Irreducible principal series of finite SL2 Mackey inner product for the finite SL2 principal series 34

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