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arXiv · 2303.14757

Models of representations for classical series of Lie algebras

D. V. Artamonov
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Abstract

A model of representations of a Lie algebra is a representation which a direct sum of all irreducible finite dimensional representations taken with multiplicity $1$. In the paper an explicit construction of a model of representation for all series of classical Lie algebras is given. The construction does not differ much for different series. The space of the model is constructed as a space of polynomial solutions of a system of partial differential equations. The equations in this system are constructed form relations between minors of matrices from the corresponding Lie group. This system has a simplification which is very close to the GKZ system, that is satisfied by $A$-hypergeometric functions.

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D. V. Artamonov. 2024-04-07. Models of representations for classical series of Lie algebras. https://doi.org/10.4213/im9150e

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