Decomposition of spinor groups by the involution σ' in exceptional Lie groups

Details Decomposition of spinor groups by the involution σ' in exceptional Lie groups Decomposition of spinor groups by the involution σ' in exceptional Lie groups

2010-12-18

arxiv.org/abs/1012.4069v1

Math. J. Okayama Univ. 44(2002), 1-27

Mathematics

Differential Geometry

24pages

Scientific paper

The compact exceptional Lie groups F4, E6, E7 and E8 have spinor groups as a subgroup as follows: E8 \supset Ss(16) \supset Spin(15) \supset Spin(14) \supset Spin(13), E7 \supset Spin(12) \supset Spin(11), E6 \supset Spin(10), F4 \supset Spin(9) \supset Spin(8) \supset Spin(7) \supset \cdot \cdot \cdot \supset Spin(1) \ni 1. We know the involution {\sigma}' induced an element {\sigma}' \in Spin(8) \subset F4 \subset E6 \subset E7 \subset E8. Now, in this paper, we determine the group structures of (Spin(n)){\sigma}' which are the fixed subgroups by the involution {\sigma}'.

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