TL;DR
This paper establishes a new multiplicity formula for K-types in irreducible representations of real reductive groups, linking K-characters to Harish-Chandra characters through a local trace formula.
Contribution
It introduces a simple local trace formula that enables the derivation of a comprehensive K-type multiplicity formula for all irreducible representations.
Findings
Derived a multiplicity formula relating K-characters and Harish-Chandra characters
Proved the formula for all irreducible representations of real reductive groups
Established a simple local trace formula for real reductive groups
Abstract
In this paper, by proving a simple local trace formula for real reductive groups, we prove a multiplicity formula of K-types for all irreducible representations of real reductive groups. This multiplicity formula expresses the K-characters in terms of the Harish-Chandra characters.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory