Generalized Versality, Special Points, and Resolvent Degree for the Sporadic Groups

Web Page for Generalized Versality, Special Points, and Resolvent Degree for the Sporadic Groups

This paper uses computations completed in SageMath [SageMath2022] by accessing GAP [GAP2022]. The SageMath script compute_molien.sage lets you pick a sporadic group G and either

computes the Molien series M (ρ_G;z) as a rational function, prints the numerator p_G(z) and the denominator q_G(z), and stores p_G(z) and q_G(z) in the file G_output.txt ; or

takes in the data for G from the GAP character table library (saved in the file G_data.txt) and computes the first 20 coefficients m_1(ρ_G), . . . , m_{20}(ρ_G) of the Molien series M (ρ_G;t), prints m_1(ρ_G), . . . , m_{20}(ρ_G) , and stores m_1(ρ_G), . . . , m_{20}(ρ_G) in the file G_output.txt.

Outcome 1 happens when G = M11, M12, M22, M23, M24, Co3, Co2, Co1, J1, J2, J3, Suz, HS, McL, Ru, or He.

Outcome 2 happens when G = J4, Fi22, Fi23, Fi24', HN, Th, O'N, Ly, B, and M.

Here are the data files, output files, the script, and a ZIP file containing all aforementioned files:

ZIP File

Script File

Output Files (Rational Functions)