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

School of Mathematical Sciences

Shanghai University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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).

Original language	English
Article number	084
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	13
DOIs	https://doi.org/10.3842/SIGMA.2017.084
State	Published - 27 Oct 2017

Keywords

Differential calculus
Module algebra
Quantum differential operators
Quantum symplectic group
Quantum symplectic space

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10.3842/SIGMA.2017.084

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abstract = "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{\textquoteright}s braid automorphisms of Uq(sp2n).",

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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).

KW - Differential calculus

KW - Module algebra

KW - Quantum differential operators

KW - Quantum symplectic group

KW - Quantum symplectic space

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ER -

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

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Keywords

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