Realization of quantum symplectic group O(Spq(8)) via vector representation of Uq(sp(8))
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摘要: Jantzen[1]利用A型李代数A2的量子包络代数Uq(sl2(C)),借助于其表示论并利用R-矩阵的方法给出了SLq(2)的定义关系式.本文对结构更为复杂的C型李代数做了类似的研究,通过Uq(sp(8))的表示理论实现了O(Spq(8))的定义关系式.Abstract: To the quantum enveloping algebra Uq(sl2(C)) of type A Lie algebra A2, Jantzen gave the defining relations of SLq(2) arising from the representations of Uq(sl2(C)) by the R-matrix. This paper studied the similar question to Uq(sp(8)) of type C Lie algebra sp(8) which is more difficult than type A, and gave the realization of O(Spq(8)) arising from the representations of Uq(sp(8)) via Jantzen's approach.
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