Hiss and Malle tables of low-dimensional represenations of quasi-simple groups

Note

This folder is not included as part of the Python package.

Warning

(11/09/2025) Due to a code bug, the complete and omissions tables lack the representations of the alternating group \(A_5\), this will be in the next table update.

Introduction

In 2001, Hiss and Malle [[1]] published a table containing all absolutely irreducible representations of quasi-simple groups of dimension at most 250, excluding those of groups of Lie type in their defining characteristic. See [[1], Theorem 1.1] for the technical details.

In 2002, a corrigendum [[2]] was published completing the list.

It is important to note that the table [[2], Table 2] contains deliberate omissions of some representations. These include:

  • The \(n-1\) or \(n-2\)-dimensional representations of alternating groups (depending on the characteristic of the base field).

  • The representations of PSL\((2,q)\) for \(q < 499\).

For more information on the omissions, see [[1], Table 2] and [[1], \(\S\) 6].

Contents of Hiss_Malle_table

We provide a digitalized version of table [[2], Table 2] in the following formats:

  • Hiss_Malle_table.tex: LaTeX file containing the table, uses the package longtables to break the table into multiple pages.

  • Hiss_Malle_table.csv: CSV file containing the table, the LaTeX $ symbol have been deleted for easier reading.

  • Hiss_Malle_table.md: Markdown file containing the table.

  • Hiss_Malle_table.txt: Plain text file containing the table in an ASCII table format, the LaTeX $ symbol have been deleted for easier reading.

For a JSON version of the table, see DataProcessingScripts/Hiss_Malle_table_data.json. Note that this JSON file contains additional data fields to those in the files above.

The table has been generated using the AI tool Mathpix as a base. After the first import, the table has been manually corrected. In the process, we have also renamed the groups to one of the notations used in FiSGO. See the SimpleGroups.SimpleGroup.latex_name method documentation for more details on the naming conventions used.

Contents of Hiss_Malle_omissions

For completeness, we provide an unpacked version of table [[1], Table 2], containing all omissions excluding those of groups of Lie type in their defining characteristic. The table is given in the following formats:

  • Hiss_Malle_omissions.tex: LaTeX file containing the table, uses the package longtables to break the table into multiple pages.

  • Hiss_Malle_omissions.csv: CSV file containing the table, the LaTeX $ symbol have been deleted for easier reading.

  • Hiss_Malle_omissions.md: Markdown file containing the table.

  • Hiss_Malle_omissions.txt: Plain text file containing the table in an ASCII table format, the LaTeX $ symbol have been deleted for easier reading.

For a JSON version of the table, see DataProcessingScripts/Hiss_Malle_missing_data.json. Note that this JSON file contains additional data fields to those in the files above.

This table has been generated using the formulas given in [[1], Table 2] for all the omissions listed above, taking into account not to produce redundacies according to what is stated in [[1], \(\S\) 6]. The scripts used to generate and treat the data can be found in DataProcessingScripts/ by the name Hiss_Malle_missing_data.py and Hiss_Malle_omissions_table.py.

Contents of Hiss_Malle_complete

We provide a complete version of table [[2], Table 2] (excluding those of groups of Lie type in their defining characteristic) in the following formats:

  • Hiss_Malle_complete.tex: LaTeX file containing the table, uses the package longtables to break the table into multiple pages.

  • Hiss_Malle_complete.csv: CSV file containing the table, the LaTeX $ symbol have been deleted for easier reading.

  • Hiss_Malle_complete.md: Markdown file containing the table.

  • Hiss_Malle_complete.txt: Plain text file containing the table in an ASCII table format, the LaTeX $ symbol have been deleted for easier reading..

For a JSON version of the table, see DataProcessingScripts/Hiss_Malle_data.json. Note that this JSON file contains additional data fields to those in the files above.

References