Explicit Plancherel Formula for the Space of Symplectic Forms

An Explicit Formula for Local Densities of Quadratic Forms

Let S and T be two positive definite integral matrices of rank m and n respectively. It is an ancient but still very challenging problem to determine how many times S can represent T , i.e., the number of integral matrices X with XSX = T . However, Siegel proved in his celebrated paper ([Si1]) that certain weighted averages of these numbers over the genus of S can be expressed as the Euler prod...

Plancherel Formula for the 2 x 2 Real Unimodular Group.

The plancherel formula for sl(2) over a local field.

More than two decades ago, in his classical paper on the irreducible unitary representations of the Lorentz group, V. Bargmann initiated the concrete study of Fourier analysis on real Lie groups and obtained the analogue of the classical Fourier expansion theorem in the case of the Lorentz group. Since then the general theory for real semisimple Lie groups has been extensively developed, chiefl...

Uperieure S Ormale N Ecole Département De Mathématiques Et Applications a Plancherel Formula on Sp 4 a Plancherel Formula on Sp 4 a Plancherel Formula on Sp 4

In HC], Harish-Chandra derived the Plancherel formula on p-adic groups. However, to have an explicit formula, one will have to compute the measures appearing in the formula. Here, we compute Plancherel measures on Sp 4 over p-adic elds explicitly.

PLANCHEREL MEASURE FOR GL(n): EXPLICIT FORMULAS AND BERNSTEIN DECOMPOSITION

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, . ...