Skip to main content
4 events
when toggle format what by license comment
Jun 2, 2011 at 19:43 history edited Igor Khavkine CC BY-SA 3.0
Fixed typo (V should have been C^3).
Jun 2, 2011 at 14:31 comment added Paul Siegel This extends to a representation of the Clifford algebra of $V$ on $S$ which in turn restricts to the spin representation of $Spin(V) \subseteq Cl(V)$. Some or all of this might only be valid for even dimensional $V$; I can't quite remember. But in the even dimensional case the spin representation is graded, and the direct summands each carry an irreducible representation of the spin group in one dimension lower.
Jun 2, 2011 at 14:26 comment added Paul Siegel The following observation should show how to generalize your answer to higher dimensions. Let $V$ be a real vector space and let $P$ be a polarization of $V \otimes \mathbb{C}$, i.e. a maximal isotropic subspace, i.e. an isotropic subspace such that $V \otimes \mathbb{C} = P \oplus \overline{P}$. Let $S$ denote the exterior algebra of $P$, and define an action of $V$ on $S$ by allowing a vector $v$ to act as exterior product with $v$ minus interior product with $v$ (up to a constant - the square root of 2, I think).
Jun 2, 2011 at 13:04 history answered Igor Khavkine CC BY-SA 3.0