Canonical Semi-Invariants and the Plancherel Formula for Parabolic Groups

A Bound for Canonical Dimension of the (semi-)spinor Groups

Using the theory of non-negative intersections, duality of the Schubert varieties, and Pieri type formula for the varieties of maximal totally isotropic subspaces, we get an upper bound for canonical dimension cd(Spinn) of the spinor group Spinn. A lower bound is given by the canonical 2-dimension cd2(Spinn), computed in [10]. If n or n + 1 is a power of 2, no space is left between these two bo...

Plancherel Formula for the 2 x 2 Real Unimodular Group.

Dunkl Operators and Canonical Invariants of Reflection Groups

Using Dunkl operators, we introduce a continuous family of canonical invariants of finite reflection groups. We verify that the elementary canonical invariants of the symmetric group are deformations of the elementary symmetric polynomials. We also compute the canonical invariants for all dihedral groups as certain hypergeometric functions.

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.