The question is as the title says: If $W$ and $V$ are vector spaces what is $\Pi(W \oplus V)$? This is motivated from Costello's notes on supersymmetric field theories in 2 and 4 dimensions. There the supersymmetry algebra in the odd part is given as $$ \Pi(S_{+} \otimes W \oplus S_- \otimes W^{*}) $$ Where $S=S_{+} \oplus S_{-}$ a spinorial representation and $W,W^*$ a vector space and its dual. What does this $\Pi$ stand for? I have been told it might be related to parity but I am not sure in what way.
2026-03-30 23:30:29.1774913429
If $W$ and $V$ are vector spaces what is $\Pi(W \oplus V)$?
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