# Tagged Questions

**2**

votes

**1**answer

155 views

### 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 ...

**4**

votes

**0**answers

200 views

### 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 ...

**2**

votes

**1**answer

671 views

### 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 ...

**1**

vote

**3**answers

404 views

### Fourier Series for the Heisenberg Nilmanifold

So the Heisenberg nilmanifold is an addition rule on triples $(a,b,c) + (x,y,z) \equiv (a+x, b+y + m\; xc ,c+z)$. This rule is associative and
$$ n(a,b,c) = \left(na, nb + m\frac{n(n-1)}{2}ac, ...

**20**

votes

**1**answer

787 views

### Majorization and Schur Polynomials

Let me first define the majorization order (or dominance order) on partitions as $\lambda \succeq \mu$ iff $$\sum _{i=1}^{k}\lambda_i \geq \sum_{i=1}^{k}\mu_i$$ for all $1\le k\le l-1$ and ...

**4**

votes

**3**answers

2k views

### 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 ...

**4**

votes

**1**answer

447 views

### Differential operators preserving the space of harmonic functions (aka higher symmetries of the Laplacian)

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 ...

**5**

votes

**3**answers

799 views

### Reading for finite Fourier Analysis

Can anyone recommend some good reading for Fourier Analysis (and the Fourier transform) over finite abelian groups? I've found it given brief descriptions in both books on representation theory and on ...