Large products of double cosets for symmetric subgroups
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915973048565760 |
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| author | Pawlowski, Brendan |
| author_facet | Pawlowski, Brendan |
| contents | We consider the problem of classifying pairs $x,y \in G$ such that $K x K y K = G$ where $G$ is a simple compact connected Lie group and $K$ is a symmetric subgroup. We give a necessary condition on $x,y$ for all simply connected $G$, and a complete classification when $G = \operatorname{SU}(n)$ and any symmetric $K \subseteq G$ except the type AIII case $K \simeq \operatorname{S}(\operatorname{U}(p) \times \operatorname{U}(n-p))$ with $p \neq n/2$. We also present some applications of these results to gate decompositions in quantum computing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07850 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Large products of double cosets for symmetric subgroups Pawlowski, Brendan Group Theory Combinatorics We consider the problem of classifying pairs $x,y \in G$ such that $K x K y K = G$ where $G$ is a simple compact connected Lie group and $K$ is a symmetric subgroup. We give a necessary condition on $x,y$ for all simply connected $G$, and a complete classification when $G = \operatorname{SU}(n)$ and any symmetric $K \subseteq G$ except the type AIII case $K \simeq \operatorname{S}(\operatorname{U}(p) \times \operatorname{U}(n-p))$ with $p \neq n/2$. We also present some applications of these results to gate decompositions in quantum computing. |
| title | Large products of double cosets for symmetric subgroups |
| topic | Group Theory Combinatorics |
| url | https://arxiv.org/abs/2604.07850 |