Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9496447 | Journal of Number Theory | 2005 | 41 Pages |
Abstract
Let F be a nonarchimedean local field, let D be a division algebra over F, let GL(n)=GL(n,F). 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,â¦,mt, exponents e1,â¦,et, torsion numbers r1,â¦,rt, formal degrees d1,â¦,dt and conductors f11,â¦,ftt. We provide explicit formulas for the Bernstein component νΩ of Plancherel measure in terms of the fundamental invariants. We prove a transfer-of-measure formula for GL(n) and establish some new formal degree formulas. We derive, via the Jacquet-Langlands correspondence, the explicit Plancherel formula for GL(m,D).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Anne-Marie Aubert, Roger Plymen,