# transformation of symplectic structure by a matrix

Suppose that in canonical symplectic basis $e_1,e_2,f_1,f_2$ we have $$\Omega=pf_1^*\wedge f_2^*+qe_1^*\wedge e_2^*+r(e_1^*\wedge f_2^*+e_2^*\wedge f_1^*)+s(e_1^*\wedge f_1^*-e_2^*\wedge f_2^*)$$ Let $A_t$ be transformation of symplectic structure that depend on the real parameter $t$ and in the basis of $e_1,e_2, f_1, f_2$ has the following form:

$\begin{vmatrix} 1& 0& 0& t\\ 0& 1& t& 0\\ 0& 0& 1& t\\ 0& 0& 0& 1\\ \end{vmatrix}$

so $A_t$ how act on $\Omega$? in fact how can we find ?s

$(p,q,r,s)\overset{A_t}{\rightarrow}(?,?,?,?)$

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