三角KZB算子的本征函数范数
Norms of eigenfunctions to trigonometric KZB operators
摘要：
设$g$是单李代数，$V[0]=V_1\otimes...\otimes V_n[0]$是$g$ -模的张量积的零权子空间.三角KZB算子是作用于$g$的Cartan子代数上的$V[0]$ -值函数的交换微分算子.利用Bethe变换构造了该算子的亚纯本征函数。我们在一个合适的函数空间上引入一个标量积，使得算子成为对称的，并且Bethe特征函数的范数的平方等于主函数在相应的临界点的Hessian。
英文摘要：
Let $g$ be a simple Lie algebra and $V[0]=V_1\otimes...\otimes V_n[0]$ the zero weight subspace of a tensor product of $g$-modules. The trigonometric KZB operators are commuting differential operators acting on $V[0]$-valued functions on the Cartan subalgebra of $g$. Meromorphic eigenfunctions to the operators are constructed by the Bethe ansatz. We introduce a scalar product on a suitable space of functions such that the operators become symmetric, and the square of the norm of a Bethe eigenfunction equals the Hessian of the master function at the corresponding critical point.
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