Representation theory, Radon transform and the heat equation on a Riemannian symmetric space

Gestur Olafsson; Henrik Schlichtkrull

Home/Archive/arXiv

arXiv · 0707.0803

Representation theory, Radon transform and the heat equation on a Riemannian symmetric space

Gestur Olafsson·Henrik Schlichtkrull

View original source ↗Read source document ↗Export metadata ↓

Abstract

Let X=G/K be a Riemannian symmetric space of the noncompact type. We give a short exposition of the representation theory related to X, and discuss its holomorphic extension to the complex crown, a G-invariant subdomain in the complexified symmetric space X_\C=G_\C/K_\C. Applications to the heat transform and the Radon transform for X are given.

Explore related subjects

math.RT

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Gestur Olafsson, Henrik Schlichtkrull. 2007-07-05. Representation theory, Radon transform and the heat equation on a Riemannian symmetric space. https://arxiv.org/abs/0707.0803

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

On the $θ$-split side of the local relative trace formula

The author derives an expression for one side of the local relative trace formula, at the level of Lie algebras, by combining methods of Arthur and Harish-Chandra with the structure theory for reductive symmetric spaces.

math.RT↗

arXiv2026

Semi-infinite parabolic IC-sheaf II: the Ran space version

This paper is a sequel to arXiv:2310.0638. Let G be a split reductive group. We define the parabolic semi-infinite category on the Ran version of the affine Grassmanian Gr_{G,Ran}. We study the semi-infinite parabolic IC-sheaf in this category. We provide several descriptions of this object, one as certain colimit, another as an intermediate extension in certain category. We relate the global and local semi-infinite categories of sheaves. We also relate the intersection cohomology sheaf of the Drinfeld compactification of Bun_P with the semi-infinite parabolic IC-sheaf.

math.RT↗

arXiv2026

Unipotent representations and the categorical trace of Frobenius

We give a new proof of the classification of unipotent representations for split finite groups of Lie type. To do this, we first construct an (infinity, 2)-categorification of Lusztig's map from the Hecke algebra to the asymptotic algebra. Then we use the theory of weights to show that it induces an isomorphism after applying trace of Frobenius.

math.RT↗