Realization of Uq(Sp2n) within the differential algebra on quantum symplectic space

Jiao Zhang; Naihong Hu

doi:10.3842/SIGMA.2017.084

Realization of U_q(Sp_2n) within the differential algebra on quantum symplectic space

Jiao Zhang
, Naihong Hu

数学科学学院

Shanghai University

科研成果: 期刊稿件 › 文章 › 同行评审

4 引用（Scopus）

摘要

We realize the Hopf algebra U_q(sp_2n) as an algebra of quantum differential operators on the quantum symplectic space χ(f_s;R) and prove that χ(fs;R) is a U_q(sp_2n)-module algebra whose irreducible summands are just its homogeneous subspaces. We give a coherence realization for all the positive root vectors under the actions of Lusztig’s braid automorphisms of U_q(sp_2n).

源语言	英语
期刊论文编号	084
期刊	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
卷	13
DOI	https://doi.org/10.3842/SIGMA.2017.084
出版状态	已出版 - 27 10月 2017

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10.3842/SIGMA.2017.084

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引用此

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AB - We realize the Hopf algebra Uq(sp2n) as an algebra of quantum differential operators on the quantum symplectic space χ(fs;R) and prove that χ(fs;R) is a Uq(sp2n)-module algebra whose irreducible summands are just its homogeneous subspaces. We give a coherence realization for all the positive root vectors under the actions of Lusztig’s braid automorphisms of Uq(sp2n).

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KW - Module algebra

KW - Quantum differential operators

KW - Quantum symplectic group

KW - Quantum symplectic space

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Realization of Uq(Sp2n) within the differential algebra on quantum symplectic space

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Realization of U_q(Sp_2n) within the differential algebra on quantum symplectic space