Hypercube subgroups of (outer) reduced Weyl groups of the Cuntz algebras
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909995764809728 |
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| author | Brenti, Francesco Conti, Roberto Nenashev, Gleb |
| author_facet | Brenti, Francesco Conti, Roberto Nenashev, Gleb |
| contents | We develop some tools, of an algebraic and combinatorial nature, which enable us to obtain a detailed description of certain quadratic subgroups of the (outer) reduced Weyl group of the Cuntz algebra ${\mathcal O}_n$. In particular, for $n=4$ our findings give a self-contained theoretical interpretation of the groups tabulated in [AJS18], which were obtained with the help of a computer. For each of these groups we provide a set of generators. A prominent role in our analysis is played by a certain family of subgroups of the symmetric group of a discrete square which we call bicompatible. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_13952 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hypercube subgroups of (outer) reduced Weyl groups of the Cuntz algebras Brenti, Francesco Conti, Roberto Nenashev, Gleb Operator Algebras Mathematical Physics Combinatorics Functional Analysis Group Theory 05E16, 05A05, 05A15 (Primary), 46L40, 05E10 (Secondary) We develop some tools, of an algebraic and combinatorial nature, which enable us to obtain a detailed description of certain quadratic subgroups of the (outer) reduced Weyl group of the Cuntz algebra ${\mathcal O}_n$. In particular, for $n=4$ our findings give a self-contained theoretical interpretation of the groups tabulated in [AJS18], which were obtained with the help of a computer. For each of these groups we provide a set of generators. A prominent role in our analysis is played by a certain family of subgroups of the symmetric group of a discrete square which we call bicompatible. |
| title | Hypercube subgroups of (outer) reduced Weyl groups of the Cuntz algebras |
| topic | Operator Algebras Mathematical Physics Combinatorics Functional Analysis Group Theory 05E16, 05A05, 05A15 (Primary), 46L40, 05E10 (Secondary) |
| url | https://arxiv.org/abs/2601.13952 |