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Volume 189, No. 1 (1999), 179-199
Nanhua Xi
A commutation formula for root vectors in quantized enveloping algebras
Abstract:
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.
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