Operator product formula for a special Macdonald function
首发时间:2017-12-06
Abstract:In this paper, we construct two sets of vertex operators $S_+$ and $S_-$ from a direct sum of two sets of Heisenberg algebras. Then by calculating the vacuum expectation value of some products of vertex operators, we get Macdonald function in special variables $x_i=t^{i-1}$ ($i=0, 1, 2, \cdots$). Hence we obtain the operator product formula for a special Macdonald function $P_{\lambda}(1, t, \cdots, t^{n-1}; q, t)$ when $n$ is finite as well as when $n$ goes to infinity.
keywords: Mathematical physics, Macdonald function, vertex operator
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特殊麦克多瑙函数的算子乘积公式
摘要:本文通过两个海森堡代数的直和构造了两类顶点算子$S_+$和$S_-$。在计算了某些顶点算子的真空期望值之后,给出了特殊变量 $x_i=t^{i-1}$ ($i=0, 1, 2, \cdots$)下的麦克多瑙函数。由此我们构造了特殊麦克多瑙函数$P_{\lambda}(1, t, \cdots, t^{n-1}; q, t)$的算子乘积公式,对于有限变量与无穷变量都给出了相应的公式。
关键词: 数学物理, 麦克多瑙函数,顶点算子
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