Uniformity and isotypic smallness for quantum-group representations
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915891717865472 |
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| author | Chirvasitu, Alexandru |
| author_facet | Chirvasitu, Alexandru |
| contents | Compact-group representations on Banach spaces are known to be norm-continuous precisely when they have finite spectra. For a quantum group with continuous-function algebra $\mathcal{C}(\mathbb{G})$ norm continuity can be cast analogously as the bounded weak$^*$-norm continuity of the representation's attached map $\mathcal{C}(\mathbb{G})^*\to \mathrm{End}(E)$. While the uniformity/isotypic finiteness equivalence no longer holds generally, it does for compact quantum groups either coamenable or having dimension-bounded irreducible representations. This generalizes the aforementioned classical variant, providing two independent quantum-specific mechanisms of recovering it. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_24855 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uniformity and isotypic smallness for quantum-group representations Chirvasitu, Alexandru Operator Algebras Functional Analysis Quantum Algebra Representation Theory 46L67, 20G42, 46A32, 47B01, 54E15, 54A20, 22D25, 22D12 Compact-group representations on Banach spaces are known to be norm-continuous precisely when they have finite spectra. For a quantum group with continuous-function algebra $\mathcal{C}(\mathbb{G})$ norm continuity can be cast analogously as the bounded weak$^*$-norm continuity of the representation's attached map $\mathcal{C}(\mathbb{G})^*\to \mathrm{End}(E)$. While the uniformity/isotypic finiteness equivalence no longer holds generally, it does for compact quantum groups either coamenable or having dimension-bounded irreducible representations. This generalizes the aforementioned classical variant, providing two independent quantum-specific mechanisms of recovering it. |
| title | Uniformity and isotypic smallness for quantum-group representations |
| topic | Operator Algebras Functional Analysis Quantum Algebra Representation Theory 46L67, 20G42, 46A32, 47B01, 54E15, 54A20, 22D25, 22D12 |
| url | https://arxiv.org/abs/2603.24855 |