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On the K-types of certain families of unitary highest weight representations of Hermitian Lie groups
Abstract
Let (g, k) be the complexication of a Hermitian symmetric pair and let γ1 <⋯<γr be the Harish-Chandra strongly orthogonal roots, with γ1 the lowest non-compact root, and let ζ be the normalized central character of k. We consider the unitary highest weight representations L(λ(x)) of $\mathfrak g $ of highest weights of the form λ(x)=−kγ1 −xζ, x∈ℝ. In particular, we are interested in the case x=a, the last reduction point in the analytic continuation in x. We prove that L(−kγ1−a ζ), k≥ 1, is K-multiplicity free and we describe all its K-types.
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BibTeX
@misc{zic2026ktypes,
title = {{On the $K$-types of certain families of unitary highest weight representations of Hermitian Lie groups}},
author = {Pavle Pand\v zić and Genkai Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04505},
eprint = {2610.04505},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04505},
}
RIS
TY - UNPB
TI - On the K-types of certain families of unitary highest weight representations of Hermitian Lie groups
AU - Pavle Pand\v zić
AU - Genkai Zhang
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.04505
UR - https://arxiv.org/abs/2610.04505
AB - Let (g, k) be the complexication of a Hermitian symmetric pair and let γ_1 <⋯<γ_r be the Harish-Chandra strongly orthogonal roots, with γ_1 the lowest non-compact root, and let ζ be the normalized central character of k. We consider the unitary highest weight representations L(λ(x)) of $\mathfrak g $ of highest weights of the form λ(x)=−kγ_1 −xζ, x∈ℝ. In particular, we are interested in the case x=a, the last reduction point in the analytic continuation in x. We prove that L(−kγ_1−a ζ), k≥ 1, is K-multiplicity free and we describe all its K-types.
ER -