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

Yury A. Neretin

doi:10.1007/s10468-018-9774-8

paper

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

arXiv:1510.03611 · doi:10.1007/s10468-018-9774-8

Abstract

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 $G L (n, C)$

34p

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

Abstract

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

Abstract

References in corpus (2)

Cited by in corpus (3)

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