561 research outputs found
Units of ring spectra and their traces in algebraic K-theory
Let GL_1(R) be the units of a commutative ring spectrum R. In this paper we
identify the composition BGL_1(R)->K(R)->THH(R)->\Omega^{\infty}(R), where K(R)
is the algebraic K-theory and THH(R) the topological Hochschild homology of R.
As a corollary we show that classes in \pi_{i-1}(R) not annihilated by the
stable Hopf map give rise to non-trivial classes in K_i(R) for i\geq 3.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol8/paper16.abs.htm
Harmonic analysis for real spherical spaces
We give an introduction to basic harmonic analysis and representation theory
for homogeneous spaces attached to a real reductive Lie group . A
special emphasis is made to the case where is real spherical.Comment: Shortened title, typos fixed, more details on dual smooth Frobenius
reciprocity (now Lemma 6.6). 38 pages, lecture notes for the Sanya meeting on
spherical varieties. To appear in Acta Math. Sinic
A local Paley-Wiener theorem for compact symmetric spaces
The Fourier coefficients of a smooth -invariant function on a compact
symmetric space are given by integration of the function against the
spherical functions. For functions with support in a neighborhood of the
origin, we describe the size of the support by means of the exponential type of
a holomorphic extension of the Fourier coefficient
Holomorphic Extension of Eigenfunctions
Let X be a Riemannian symmetric space of non-compact type. We prove a theorem
of holomorphic extension for eigenfunctions of the Laplace-Beltrami operator on
X, by techniques from the theory of partial differential equations.Comment: 8p, no figure
Representation theory, Radon transform and the heat equation on a Riemannian symmetric space
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
Braided injections and double loop spaces
We consider a framework for representing double loop spaces (and more
generally E-2 spaces) as commutative monoids. There are analogous commutative
rectifications of braided monoidal structures and we use this framework to
define iterated double deloopings. We also consider commutative rectifications
of E-infinity spaces and symmetric monoidal categories and we relate this to
the category of symmetric spectra.Comment: 34 pages, 4 figures, minor correction
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