Irreducible conjugate-symmetric $P$ with $P(\zeta X,\zeta^{-1}Y)=-P$ equals $X^mA(XY)+Y^m\bar A(XY)$, $A$ nonconstant

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Irreducible conjugate-symmetric $P$ with $P(\zeta X,\zeta^{-1}Y)=-P$ equals $X^mA(XY)+Y^m\bar A(XY)$, $A$ nonconstant · Prove2Me