  Let $K[X_d,Y_d]=K[x_1,\ldots,x_d,y_1,\ldots,y_d]$ be the polynomial algebra
in $2d$ variables over a field $K$ of characteristic 0 and let $\delta$ be the
derivation of $K[X_d,Y_d]$ defined by $\delta(y_i)=x_i$, $\delta(x_i)=0$,
$i=1,\ldots,d$. In 1994 Nowicki conjectured that the algebra
$K[X_d,Y_d]^{\delta}$ of constants of $\delta$ is generated by $X_d$ and
$x_iy_j-y_ix_j$ for all $1\leq i<j\leq d$. The affirmative answer was given by
several authors using different ideas. In the present paper we give another
proof of the conjecture based on representation theory of the general linear
group $GL_2(K)$.
