The orthogonal group for signature is sometimes called the Narain group or generalized T-duality group for the role that it plays in T-duality of type II string theory. See also at type II geometry.
Structure group of generalized tangent bundle
For a smooth manifold, the generalized tangent bundle has as structure group the Narain group.
Maximal compact subgroup
The maximal compact subgroup of the Narain group is the product group . A reduction of the structure group of the generalized tangent bundle along the inclusion defines a type II geometry.
|group||symbol||universal cover||symbol||higher cover||symbol|
|orthogonal group||Pin group||Tring group|
|special orthogonal group||Spin group||String group|
|anti de Sitter group|
|Poincaré group||Poincaré spin group|
|super Poincaré group|