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Corpus ID: 128358733

Quantum Boson Algebra and Poisson Geometry of the Flag Variety

@article{Li2019QuantumBA,
title={Quantum Boson Algebra and Poisson Geometry of the Flag Variety},
author={Y. Li},
journal={arXiv: Quantum Algebra},
year={2019}
}

In his work on crystal bases \cite{Kas}, Kashiwara introduced a certain degeneration of the quantized universal enveloping algebra of a semi-simple Lie algebra $\mathfrak g$, which he called a quantum boson algebra. In this paper, we construct Kashiwara operators associated to all positive roots and use them to define a variant of Kashiwara's quantum boson algebra. We show that a quasi-classical limit of the positive half of our variant is a Poisson algebra of the form $(P \simeq \mathbb C… CONTINUE READING