A Plancherel Formula for Parabolic Subgroups

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.

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...

Plancherel Formula for the 2 x 2 Real Unimodular Group.

A Parabolic Almost Monotonicity Formula

We prove the parabolic counterpart of the almost monotonicity formula of Caffarelli, Jerison and Kening for pairs of functions u±(x, s) in the strip S1 = Rn × (−1, 0] satisfying u± ≥ 0, (∆− ∂s)u± ≥ −1, u+ · u− = 0 in S1. We also establish a localized version of the formula as well as prove one of its variants. At the end of the paper we give an application to a free boundary problem related to ...

Quasi-parabolic Siegel Formula

The result of Siegel that the Tamagawa number of SLr over a function field is 1 has an expression purely in terms of vector bundles on a curve, which is known as the Siegel formula. We prove an analogous formula for vector bundles with quasi-parabolic structures. This formula can be used to calculate the betti numbers of the moduli of parabolic vector bundles using the Weil conjucture.