Restriction of representations of $GL(n+1,C)$ to $GL(n,C)$ and action of the Lie overalgebra

Consider a restriction of an irreducible finite dimensional holomorphic representation of $\GL (n + 1, C)$ to the subgroup $G L (n, C)$ (it is determined by the Gelfand-Tsetlin branching rule). We write explicitly formulas for generators of the Lie algebra $g l (n + 1)$ in the direct sum of representations of $\GL (n, C)$ . Nontrivial generators act as differential-difference operators, the differential part has order $(n - 1)$ , the difference part acts on the space of parameters (highest weights) of representations. We also formulate a conjecture about unitary principal series of $G L (n, C)$

Restriction of representations of $G L (n + 1, C)$ to $G L (n, C)$ and action of the Lie overalgebra

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Restriction of representations of $G L (n + 1, C)$ to $G L (n, C)$ and action of the Lie overalgebra

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Restriction of representations of GL(n+1,C)GL(n+1,C) to GL(n,C)GL(n,C) and action of the Lie overalgebra

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Restriction of representations of GL(n+1,C)GL(n+1,C) to GL(n,C)GL(n,C) and action of the Lie overalgebra

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Restriction of representations of $G L (n + 1, C)$ to $G L (n, C)$ and action of the Lie overalgebra

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Restriction of representations of $G L (n + 1, C)$ to $G L (n, C)$ and action of the Lie overalgebra

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