Papers

Enumerating Finite Braid Group Orbits on SL(2, C)-Character Varieties: Here is a link to the pdf.

Code

If you find any errors or run into trouble please email me: amalrose dot vayalinkal at mail dot utoronto dot ca

Magma code for middle convolution. Following description of middle convolution in this paper by Dettweiler and Reiter (2018). The group W in the code is a complex reflection group, but any matrix group will work. The code may be updated with more comments or examples some day.

Searching For Nice Tuples. This is code for searching the finite complex reflection groups for tuples of matrices so that their middle convolution wil be of rank 2.

Braid Group Orbit for 4-Tuples. This is code for computing the orbit of 4-tuples of matrices in SL(2, C) under the action of the spherical braid group when this orbit is known to be finite. The code at the end is for checking tuples of the same 'type' from the finite complex reflection groups do not produce new orbits after middle convolution. Note that to check types the middle convolution code must already be loaded from the file above. Here is the same code for 5-tuples in SL(2, C).

Comparing with Other Classificaitons. Here is some code for computing signatures of tuples in a finite orbit so one can check if they correspond to any listed in the classification of finite orbits given in this paper by Lisovy-Tykhyy (2014) or in this paper by Tykhyy (2022).