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Q: Coset representatives for $wPw^{-1} \cap P' \backslash P'$ for parabolic subgroups $P'$ and $P$?

D_SI'm going through the calculation of the constant term of Eisenstein series in Moeglin and Waldsburger's Spectral Decomposition and Eisenstein series book (section II.1.7), and am confused on a small detail. Let $P = MN$ and $P' = M'N'$ be standard parabolic subgroups of a connected, reductive g...

Eisenstein series, named after German mathematician Gotthold Eisenstein, are particular modular forms with infinite series expansions that may be written down directly. Originally defined for the modular group, Eisenstein series can be generalized in the theory of automorphic forms. == Eisenstein series for the modular group == Let τ be a complex number with strictly positive imaginary part. Define the holomorphic Eisenstein series G2k(τ) of weight 2k, where k ≥ 2 is an integer, by the following series: G 2 k...
 

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