Essential dimension of semisimple groups of type B

We determine the essential dimension of an arbitrary semisim-ple group of type B of the form G = (Spin(2n1 + 1) x & BULL; & BULL; & BULL; x Spin(2nm + 1))/& mu; over a field of characteristic 0, for all n1, ... , nm & GE; 7, and a central subgroup & mu; of Spin(2n1 + 1) x & BULL; & BULL; & BULL; x Spin(2nm + 1) not containing the center of Spin(2ni + 1) as a direct factor for every i = 1, ... , m.& COPY; 2023 Elsevier Inc. All rights reserved.

Automated summary

This study determines the essential dimension of an arbitrary semisimple group of type B, denoted as G, over a field of characteristic 0. The group G can be represented as (Spin(2n1 + 1) x ... x Spin(2nm + 1))/& mu;, where n1, ... , nm & GE; 7, and & mu; is a central subgroup of Spin(2n1 + 1) x ... x Spin(2nm + 1) that does not contain the center of Spin(2ni + 1) as a direct factor for every i = 1, ... , m.