# Tagged Questions

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### Roots of the XXZ Bethe Ansatz equation

The XXZ spin chain Bethe Ansatz equations are a complicated system of rational function equation: \[ \left(\frac{\lambda_j + i/2}{\lambda_j - i/2} \right)^N = \prod_{l=1, l \neq j}^M ...
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### Find polynom p(z) with values in C[S_n] such that p'(z) = \sum_i (Id+(1i))/(z-i) p(z). [Knizhnik-Zamolodchikov equation for S_n]

Consider group algebra $C[S_n]$. Take any of its representation $(\pi, V)$ (for example regular). Take some complex numbers $z_i$ i=2...n. Denote as usually by $(1i)\in S_n$ the transpositions of ...
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### Bochner's Theorem and Total Positivity

Bochner's Theorem for LCA groups applied to the case of $G = U(1)$ and $G^{\vee} = \mathbb{Z}$ tells us that through the Fourier transform, probability measures on the circle are in bijection with ...
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### Spherical Harmonics - a bunch of questions about them

Hi there, Please tell me if I should divide these into individual questions next time. Short intro: Spherical Harmonics are a nice collection of functions. They are orthogonal and allow you to take ...
The article http://arxiv.org/abs/hep-th/0206233 (published in Ann. of Math. (2) 161 (2005), no. 3) deals with linear differential operators $D$ for which there exists another linear differential ...