𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Orthogonality Relations and Harmonic Forms for Semisimple Lie Groups

✍ Scribed by Robert W. Donley Jr.

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
207 KB
Volume
170
Category
Article
ISSN
0022-1236

No coin nor oath required. For personal study only.

✦ Synopsis

Let G be a connected semisimple Lie group with finite center, and suppose G contains a compact Cartan subgroup T. Certain irreducible unitary representations of G arise as spaces of harmonic forms associated to Dolbeault cohomology of line bundles over the complex homogeneous space GΓ‚T. In this work the unitary structures of these realizations are directly related to the orthogonality relations for the matrix coefficients of these representations. Using this connection, we exhibit unitary realizations of certain limits of discrete series representations of SU(2, 1) as spaces of harmonic forms.

πŸ“œ SIMILAR VOLUMES

L1Estimates for Maximal Functions and Ri
L1Estimates for Maximal Functions and Riesz Transform on Real Rank 1 Semisimple Lie Groups
✍ Takeshi Kawazoe πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 481 KB

Let G be a real rank one semisimple Lie group and K a maximal compact subgroup of G. Radial maximal operators for suitable dilations, the heat and Poisson maximal operators, and the Riesz transform, which act on K-bi-invariant functions on G, satisfy the L p -norm inequalities for p>1 and a weak typ

Heat and Harmonic Extensions for Functio
Heat and Harmonic Extensions for Function Spaces of Hardy–Sobolev–Besov Type on Symmetric Spaces and Lie Groups
✍ Leszek Skrzypczak πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 192 KB

Function spaces of Hardy Sobolev Besov type on symmetric spaces of noncompact type and unimodular Lie groups are investigated. The spaces were originally defined by uniform localization. In the paper we give a characterization of the space F s p, q (X ) and B s p, q (X ) in terms of heat and Poisson