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arXiv · 1510.03611

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

Yury A. Neretin
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Abstract

Consider a restriction of an irreducible finite dimensional holomorphic representation of $\GL(n+1,C)$ to the subgroup $GL(n,C)$ (it is determined by the Gelfand-Tsetlin branching rule). We write explicitly formulas for generators of the Lie algebra $gl(n+1)$ 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 $GL(n,C)$

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BibTeXRIS

Yury A. Neretin. 2018-02-15. Restriction of representations of $GL(n+1,C)$ to $GL(n,C)$ and action of the Lie overalgebra. https://doi.org/10.1007/s10468-018-9774-8

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