GENERALIZED GAUSS DECOMPOSITION OF TRIGONOMETRIC R-MATRICES
GENERALIZED GAUSS DECOMPOSITION OF TRIGONOMETRIC R-MATRICES
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三角R矩阵的广义高斯分解
DOI：
10.1142/s0217732395001496
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发表时间：
1994
影响因子：
1.4
通讯作者：
V. Tolstoy
中科院分区：
文献类型：
--
作者：
S. Khoroshkin;A. Stolin;V. Tolstoy
第一作者和第三作者获得的量化非扭曲仿射代数通用R矩阵的通用公式应用于量化仿射代数的零中心电荷、最高权模。展示了通用 R 矩阵如何在这些模块的张量积中产生三角 R 矩阵的高斯分解。特别是，介绍了通用 R 矩阵的当前实现。它为带有 Uq(sl2)-Verma 模张量积参数的三角 R 矩阵提供了新的通用表示。给出了对任何 Uq(ĝ) 的通用 R 矩阵的有限维表示中出现的标量因子的详细分析。我们将此标量因子解释为不可约表示的最高权重多项式的乘法双线性形式，并用无限 q 平移阶乘表示此形式。
The general formula for the universal R-matrix for quantized nontwisted affine algebras, obtained by the first and third authors, is applied to zero central charge, highest weight modules of the quantized affine algebras. It is shown how the universal R-matrix produces the Gauss decomposition of trigonometric R-matrix in tensor product of these modules. In particular, current realization of the universal R-matrix is presented. It gives a new universal presentation for the trigonometric R-matrix with a parameter in tensor product of Uq(sl2)-Verma modules. Detailed analysis of a scalar factor arising in finite-dimensional representations of the universal R-matrix for any Uq(ĝ) is given. We interpret this scalar factor as a multiplicative bilinear form on highest weight polynomials of irreducible representations and express this form in terms of infinite q-shifted factorials.