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176 views

### In what sense is the braid group $B_3$ the universal central extension of the modular group $\Gamma$?

First let's recall some definitions. Let $G$ be a perfect group, so that
$$H^2(G, A) \cong \text{Hom}(H_2(G), A)$$
for all abelian groups $A$ by universal coefficients. This means that when $A = ...

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41 views

### Action of a Drinfeld modular group on a Drinfeld symmetric space

Let $\Bbb C_\infty$ be functional field case analog of $\Bbb C$, i.e. $\Bbb C_\infty$ is the completion of the algebraic closure of the field of Laurent series $\Bbb F_q((\theta^{-1}))$, where $q$ is ...

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72 views

### Number of unimodular and singular matrices of particular type

Consider matrices of type
$$K_{r,n}=\begin{bmatrix}
a_{11} &a_{12} &\dots &a_{1n}\\
a_{21} &a_{22} &\dots &a_{2n}\\
\vdots &\vdots &\ddots &\vdots\\
a_{r1} ...