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摘要翻译：
我们证明了以下两个代数是同构的。第一个是一元线性二阶微分算子在$\c$上的方案上的函数代数$a_p$,在$z_1,...,z_n,\infty$上有规定的正则奇点，在奇点上有规定的指数$\la^{（1）},...,\la^{(n)},\la^{(\infty)},核仅由多项式组成。第二个是交换线性算子的Bethe代数，作用于有限维多项式GL_2$-模的张量积中具有最高权的奇异向量$\la^{(1)}，...，\la^{(n)}$的向量空间$\sing L_{\la^{(1)}}\\times...[\la^{(infty)}}[\la^{(infty)}]$。
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英文标题：
《Bethe algebra and algebra of functions on the space of differential
operators of order two with polynomial solutions》
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作者：
E.Mukhin, V.Tarasov and A.Varchenko
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Quantum Algebra 量子代数
分类描述：Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory
量子群，skein理论，运算代数和图解代数，量子场论
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Classical Analysis and ODEs 经典分析与颂歌
分类描述：Special functions, orthogonal polynomials, harmonic analysis, ODE's, differential relations, calculus of variations, approximations, expansions, asymptotics
特殊函数、正交多项式、调和分析、Ode、微分关系、变分法、逼近、展开、渐近
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英文摘要：
We show that the following two algebras are isomorphic. The first is the algebra $A_P$ of functions on the scheme of monic linear second-order differential operators on $\C$ with prescribed regular singular points at $z_1,..., z_n, \infty$, prescribed exponents $\La^{(1)}, ..., \La^{(n)}, \La^{(\infty)}$ at the singular points, and having the kernel consisting of polynomials only. The second is the Bethe algebra of commuting linear operators, acting on the vector space $\Sing L_{\La^{(1)}} \otimes ... \otimes L_{\La^{(n)}}[\La^{(\infty)}]$ of singular vectors of weight $\La^{(\infty)}$ in the tensor product of finite dimensional polynomial $gl_2$-modules with highest weights $\La^{(1)},..., \La^{(n)}$.
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PDF链接：
https://arxiv.org/pdf/0705.4114
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