$\newcommand\Alt{\bigwedge\nolimits}$Let $G=\operatorname{SL}(2,\Bbb C)$, and let $R$ denote the natural 2-dimensional representation of $G$ in ${\Bbb C}^2$. For an integer $p\ge 0$, write $R_p=S^p R$; then $R_1=R$ and $\dim R_p=p+1$.

Using Table 5 in the book of Onishchik and Vinberg, I computed that the representation $$ R_2\otimes\Alt^2 R_4 $$ contains the trivial representation with multiplicity one. I used the table as a black box.

Question.Let $V\subset R_2\otimes\Alt^2 R_4$ denote the corresponding one-dimensional subspace. How can one describe $V$ as a subspace?geometrically

**Motivation:** I want to consider a $\operatorname{PGL}(2,k)$-fixed trivector
$$v\in V\subset R_2\otimes\Alt^2 R_4\subset \Alt^3(R_2\oplus R_4)$$
of the 8-dimensional vector space $W=R_2\oplus R_4$
over a field $k$ of characteristic 0,
and then to twist all this using a Galois-cocycle of $\operatorname{PGL}(2,k)$. For this end I need a geometric description of $V$.

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