2012/09/19 by B. Harris, Benjamin Harris, Hongyu He +5
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.1209.4125
International Journal of Mathematics, Volume 24, Number 7, 2013
openalex publication_date 2012/09/19 · arxiv created 2013/08/07 · arxiv updated 2013/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If G is a reductive Lie group of Harish-Chandra class, H is a symmetric subgroup, and π is a discrete series representation of G, the authors give a condition on the pair (G,H) which guarantees that the direct integral decomposition of π|H contains each irreducible representation of H with finite multiplicity. In addition, if G is a reductive Lie group of Harish-Chandra class, and H⊂ G is a closed, reductive subgroup of Harish-Chandra class, the authors show that the multiplicity function in the direct integral decomposition of π|H is constant along `continuous parameters'. In obtaining these results, the authors develop a new technique for studying multiplicities in the restriction π|H via convolution with Harish-Chandra characters. This technique has the advantage of being useful for studying the continuous spectrum as well as the discrete spectrum.