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Let $GL_M$ be general linear Lie group over the complex field. Theirreducible rational representations of the group $GL_M$ are labeled by pairsof partitions $\mu$ and $\tilde\mu$ such that the total number of non-zeroparts of $\mu$ and $\tilde{\mu}$ does not exceed $M$. Let $U$ be therepresentation of $GL_M$ corresponding to such a pair. Regard the directproduct $GL_N\times GL_M$ as a subgroup of $GL_{N+M}$. Let $V$ be theirreducible rational representation of the group $GL_{N+M}$ corresponding to apair of partitions $\lambda$ and $\tilde{\lambda}$. Consider the vector space$W=Hom_{G_M}(U,V)$. It comes with a natural action of the group $GL_N$. Let $n$be sum of parts of $\lambda$ less the sum of parts of $\mu$. Let $\tilde{n}$ besum of parts of $\tilde{\lambda}$ less the sum of parts of $\tilde{\mu}$. Forany choice of two standard Young tableaux of skew shapes $\lambda/\mu$ and$\tilde{\lambda}/\tilde{\mu}$ respectively, we realize $W$ as a subspace in thetensor product of $n$ copies of the defining $N$-dimensional representation of$GL_N$, and of $\tilde{n}$ copies of the contragredient representation. Thissubspace is determined as the image of a certain linear operator $F$ in thetensor product, given by explicit multiplicative formula. When M=0 and $W=V$ isan irreducible representation of $GL_N$, we recover the classical realizationof $V$ as a subspace in the space of all traceless tensors. Then the operator$F$ can be regarded as the rational analogue of the Young symmetrizer,corresponding to the chosen standard tableau of shape $\lambda$. Even in thespecial case M=0, our formula for the operator $F$ is new. Our results areapplications of representation theory of the Yangian of the Lie algebra $gl_N$.Comment: 44 pages, final versio

Rational representations of Yangians associated with skew Young diagrams