Discrete series representations with non-tempered embedding
Bernhard Kr\"otz, Job J. Kuit, Henrik Schlichtkrull

TL;DR
This paper provides an example of a semisimple symmetric space where a specific irreducible representation exhibits different multiplicities in the spaces of square-integrable and smooth functions, highlighting nuanced representation behavior.
Contribution
It introduces a concrete example demonstrating the disparity in multiplicities of an irreducible representation in different function spaces on a symmetric space.
Findings
Multiplicity is 1 in L^2(G/H)
Multiplicity is 2 in C^∞(G/H)
Highlights differences in representation theory in symmetric spaces
Abstract
We give an example of a semisimple symmetric space and an irreducible representation of which has multiplicity 1 in and multiplicity 2 in .
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Operator Algebra Research · Advanced Topics in Algebra
