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

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arXiv · 2604.20566

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

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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.

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BibTeX RIS

Pavle Pandžić, Ana Prlić, Vladimír Souček, Vít Tuček. 2026-04-22. Unitary highest weight modules for $\mathfrak{su}(p, q)$ and $\mathfrak{so}^{*}(2n)$ with fixed integral infinitesimal character. https://arxiv.org/abs/2604.20566

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