The spin group 
,
for 
, is the connected double
cover of the special orthogonal group 
. It can be constructed inside the
group of units of the Clifford algebra of 
as products of an even number of unit vectors. Conjugation on vectors
gives an exact sequence
 |
The spinor representations of 
arise from its action through the Clifford
algebra and do not descend to 
. However, failure to descend does not characterize the
spinor representations (Woit 2017, Chs. 7 and 31).
