PLANCHEREL MEASURE FOR GL(n): EXPLICIT FORMULAS AND BERNSTEIN DECOMPOSITION
نویسنده
چکیده
Let F be a nonarchimedean local field, let GL(n) = GL(n, F ) and let ν denote Plancherel measure for GL(n). Let Ω be a component in the Bernstein variety Ω(GL(n)). Then Ω yields its fundamental invariants: the cardinality q of the residue field of F , the sizes m1, . . . ,mt, exponents e1, . . . , et, torsion numbers r1, . . . , rt, formal degrees d1, . . . , dt and the Artin conductors f11, . . . , ftt. We provide explicit formulas for the Bernstein component νΩ of Plancherel measure in terms of the fundamental invariants. We also prove a transfer-of-measure formula for GL(n).
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