Essential dimension of double covers of symmetric and alternating groups
| Autor: | Reichstein, Zinovy, Shukla, Abhishek Kumar |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | I. Schur studied double covers $\widetilde{\Sym}^{\pm}_n$ and $\widetilde{\Alt}_n$ of symmetric groups $\Sym_n$ and alternating groups $\Alt_n$, respectively. Representations of these groups are closely related to projective representations of $\Sym_n$ and $\Alt_n$; there is also a close relationship between these groups and spinor groups. We study the essential dimension $\ed(\widetilde{\Sym}^{\pm}_n)$ and $\ed(\widetilde{\Alt}_n)$. We show that over a base field of characteristic $\neq 2$, $\ed(\widetilde{\Sym}^{\pm}_n)$ and $\ed(\widetilde{\Alt}_n)$ grow exponentially with $n$, similar to $\ed(\Spin_n)$. On the other case, in characteristic $2$, they grow sublinearly, similar to $\ed(\Sym_n)$ and $\ed(\Alt_n)$. We give an application of our result in good characteristic to the theory of trace forms. Comment: 19 pages |
| Databáze: | arXiv |
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