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Mackey restriction formula

For

H, K \leq G

and a

K

-representation

V

,

Res_{H}^{G} Ind_{K}^{G} V ≅ ⨁_{x \in H \ G / K} Ind_{H \cap x K x^{- 1}}^{H} Res_{H \cap x K x^{- 1}}^{x K x^{- 1}} (^{x} V),

where

^{x} V (x k x^{- 1}) = V (k)

.

Table of contents 140 4
- Mackey irreducibility criterion Mackey restriction formula 40
- Bruhat decomposition of SL2 over a finite field Mackey restriction formula 79 2
  - Mackey inner product for the finite SL2 principal series Bruhat decomposition of SL2 over a finite field 53 1
    - Irreducible principal series of finite SL2 Mackey inner product for the finite SL2 principal series 34

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