A commutation formula for root vectors in quantized enveloping algebras
A commutation formula for root vectors in quantized enveloping algebras
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DOI：
10.2140/pjm.1999.189.179
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发表时间：
1999-05
影响因子：
0.6
通讯作者：
N. Xi
中科院分区：
文献类型：
--
作者：
N. Xi
根向量对于理解量子化包络代数很重要。本文建立了根向量的一个交换公式。利用这个公式，我们证明了在构造量子化包络代数的某些整基时，根系上的特定阶是不必要的（定理2.4）。此外，使用公式，我们可以表明，某些PBW基地是正交基地的双线性形式考虑柏原在他的工作晶体基地，见3.9。
Root vectors are important to understand quantized enveloping algebras. In this paper we establish a commutation formula for root vectors. By means of the formula we show that particular orders on root system are not necessary in constructing some integral bases of a quantized enveloping algebra (Theorem 2.4). Moreover using the formula we can show that certain PBW bases are orthogonal bases of the bilinear form considered by Kashiwara in his work on crystal bases, see 3.9.