Essential dimension of semisimple groups of type $B$

Abstract

We determine the essential dimension of an arbitrary semisimple group of type $B$ of the form \[G=\big(\operatorname{\mathbf{Spin}}(2n_{1}+1)\times\cdots \times \operatorname{\mathbf{Spin}}(2n_{m}+1)\big)/\boldsymbolμ\] over a field of characteristic $0$, for all $n_1,\dots ,n_m\ge 7$, and a central subgroup $\mathbf{\mu }$ of $\mathrm{Spin}(2n_1+1)\times \cdots \times \mathrm{Spin}(2n_m+1)$ not containing the center of $\mathrm{Spin}(2n_i+1)$ as a direct factor. We also find the essential dimension of $G$ for each of the following cases, where either $n_i=1$ for all $i$ or $m=2$, $n_1=1$, $2\le n_2\le 3$, $\mathbf{\mu }$ is the diagonal central subgroup for both cases.

References in corpus (1)

• Spinors and essential dimension

Cited by in corpus (1)

• Essential dimension of reductive groups via generically free representations