A Plancherel formula for the isotropic cone

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 Giambelli Formula for Isotropic Grassmannians

LetX be a symplectic or odd orthogonal Grassmannian parametrizing isotropic subspaces in a vector space equipped with a nondegenerate (skew) symmetric form. We prove a Giambelli formula which expresses an arbitrary Schubert class in H∗(X,Z) as a polynomial in certain special Schubert classes. We introduce and study theta polynomials, a family of polynomials which are positive linear combination...

A Giambelli Formula for Isotropic Partial Flag Varieties

Let G be a classical complex Lie group, P any parabolic subgroup of G, and G/P the corresponding partial flag variety. We prove an explicit nonrecursive Giambelli formula which expresses an arbitrary Schubert class in H(G/P ) as a polynomial in certain special Schubert class generators; in the even orthogonal case this depends on the main result of [BKT4]. Our formula extends to one that applie...