nLab Spin(16)

Idea

The spin group in dimension 16.

Related concepts

rotation groups in low dimensions:

Dynkin label	sp. orth. group	spin group	pin group	semi-spin group
	SO(2)	Spin(2)	Pin(2)
B1	SO(3)	Spin(3)	Pin(3)
D2	SO(4)	Spin(4)	Pin(4)
B2	SO(5)	Spin(5)	Pin(5)
D3	SO(6)	Spin(6)
B3	SO(7)	Spin(7)
D4	SO(8)	Spin(8)		SO(8)
B4	SO(9)	Spin(9)
D5	SO(10)	Spin(10)
B5	SO(11)	Spin(11)
D6	SO(12)	Spin(12)
	$\vdots$	$\vdots$
D8	SO(16)	Spin(16)		SemiSpin(16)
	$\vdots$	$\vdots$
D16	SO(32)	Spin(32)		SemiSpin(32)

see also

• Spin(5).Spin(3)

• finite rotation groups

• ADE-classification

type I' string theory

References

General

(…)

In grand unified theory

Discussion of Spin(16)-grand unified theories (traditionally called “SO(16)” GUT):

• Frank Wilczek, Anthony Zee, Families from spinors, Phys. Rev. D 25, 553 (1982) (doi:10.1103/PhysRevD.25.55310.1103/PhysRevD.25.553)

• Goran Senjanović, Frank Wilczek, Anthony Zee, Reflections on mirror fermions, Physics Letters B Volume 141, Issues 5–6, 5 July 1984, Pages 389-394 Physics Letters B (doi:10.1016/0370-2693(84)90269-7)