symmetric_group
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symmetric_group [2020/02/14 07:03] amang created |
symmetric_group [2021/11/23 11:56] (current) |
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| ====== Symmetric group ====== | ====== Symmetric group ====== | ||
| - | A **symmetric group** is any member of a certain sequence $(S_N)_{N\in \N}$ of [[classical matrix groups]]. | + | A **symmetric group** is any member of a certain sequence $(S_N)_{N\in \N}$ of [[classical orthogonal matrix groups]]. |
| ===== Definition ===== | ===== Definition ===== | ||
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| ===== Basic properties ===== | ===== Basic properties ===== | ||
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| + | The symmetric groups $(S_N)_{N\in \N}$ are an [[easy_quantum_group|easy]] family of compact matrix quantum groups, i.e., the intertwiner spaces of their corepresentation categories are induced by a [[category of partitions]]. In fact, the [[category of all partitions]] induces the corepresentation categories of $(S_N)_{N\in \N}$. It is canonically generated by $\{\crosspart,\fourpart, \singleton\}$. | ||
| ===== Representation theory ===== | ===== Representation theory ===== | ||
symmetric_group.1581663780.txt.gz ยท Last modified: 2021/11/23 11:56 (external edit)
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