Full Projective Oscillator Representations of Special Linear Lie Algebras and Combinatorial Identities
Abstract
Using the projective oscillator representation of sl(n+1) and Shen's mixed product for Witt algebras, Zhao and the second author (2011) constructed a new functor from sl(n)-Mod to sl(n+1)-Mod. In this paper, we start from n = 2 and use the functor successively to obtain a full projective oscillator realization of any finite-dimensional irreducible representation of sl(n+1). The representation formulas of all the root vectors of sl(n+1) are given in terms of first-order differential operators in n(n+1)/2 variables. One can use the result to study tensor decompositions of finite-dimensional irreducible modules by solving certain first-order linear partial differential equations, and thereby obtain the corresponding physically interested Clebsch-Gordan coefficients and exact solutions of Knizhnik-Zamolodchikov equation in WZW model of conformal field theory.
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Cite
@article{arxiv.2210.13878,
title = {Full Projective Oscillator Representations of Special Linear Lie Algebras and Combinatorial Identities},
author = {Zhenyu Zhou and Xiaoping Xu},
journal= {arXiv preprint arXiv:2210.13878},
year = {2022}
}
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36 pages