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SL2Reps

Constructing symmetric representations of SL(2,Z).

1.1

26 November 2022

Siu-Hung Ng
Email: rng@math.lsu.edu
Homepage: https://www.math.lsu.edu/~rng/
Address:
Louisiana State University, Baton Rouge, LA, 70803, USA

Yilong Wang
Email: wyl@bimsa.cn
Homepage: https://yilongwang11.github.io
Address:
Louisiana State University, Baton Rouge, LA, 70803, USA
Current: Beijing Institute of Mathematical Sciences and Applications (BIMSA), Huairou, Beijing, China

Samuel Wilson
Email: swil311@lsu.edu
Homepage: https://snw-0.github.io
Address:
Louisiana State University, Baton Rouge, LA, 70803, USA

Copyright

© 2022 by Siu-Hung Ng, Yilong Wang, and Samuel Wilson

This package is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

Acknowledgements

This project is partially supported by NSF grant DMS 1664418.

Contents

1.1 Installation

2.1 Construction

  2.1-1 Weil representations
  2.1-2 Character subspaces and primitive characters
  2.1-3 Irrep Types
  2.1-4 S and T matrices

2.2 Weil representation types

  2.2-1 Type D
  2.2-2 Type N
  2.2-3 Type R, generic cases
  2.2-4 Type R, unary and extremal cases

3 Irreducible representations of prime-power level

3.1 Representations of type D

3.1-1 SL2ModuleD
3.1-2 SL2IrrepD

3.2 Representations of type N

3.2-1 SL2ModuleN
3.2-2 SL2IrrepN

3.3 Representations of type R

  3.3-1 SL2ModuleR
  3.3-2 SL2IrrepR
  3.3-3 SL2IrrepRUnary

4 Lists of representations

4.1 Lists by degree

4.1-1 SL2IrrepsOfDegree
4.1-2 SL2IrrepsOfMaxDegree

4.2 Lists by level

4.2-1 SL2IrrepsOfLevel

4.3 Lists of exceptional representations

4.3-1 SL2IrrepsExceptional

5 Methods for testing

  5.1-1 SL2WithConjClasses
  5.1-2 SL2ChiST
  5.1-3 SL2TestPositions
  5.1-4 SL2TestSymmetry

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