Unitary highest weight modules for $\mathfrak{su}(p, q)$ and $\mathfrak{so}^{*}(2n)$ with fixed integral infinitesimal character

Pavle Pandžić; Ana Prlić; Vladimír Souček; Vít Tuček

Unitary highest weight modules for $\mathfrak{su}(p, q)$ and $\mathfrak{so}^{*}(2n)$ with fixed integral infinitesimal character

Representation Theory 2026-04-23 v1

Authors: Pavle Pandžić , Ana Prlić , Vladimír Souček , Vít Tuček

Abstract

We classify unitary highest weight modules with a given integral infinitesimal character for the real Lie algebras $\mathfrak{su}(p,q)$ and $\mathfrak{so}^*(2n)$ . We treat both regular and singular cases. For $\mathfrak{su}(p,q)$ we identify the unitarizable modules in the Hasse diagrams of the highest weight orbit. Analogous results for the other Hermitian Lie algebras were given in our earlier publications.

Keywords

unitary highest weight modules real Lie algebras infinitesimal character classification Hasse diagrams Hermitian Lie algebras

Cite

@article{arxiv.2604.20566,
  title  = {Unitary highest weight modules for $\mathfrak{su}(p, q)$ and $\mathfrak{so}^{*}(2n)$ with fixed integral infinitesimal character},
  author = {Pavle Pandžić and Ana Prlić and Vladimír Souček and Vít Tuček},
  journal= {arXiv preprint arXiv:2604.20566},
  year   = {2026}
}

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31 pages, 4 figures

Unitary highest weight modules for $\mathfrak{su}(p, q)$ and $\mathfrak{so}^{*}(2n)$ with fixed integral infinitesimal character

Abstract

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