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<h1>SL2Reps</h1>


<h2>Constructing symmetric representations of SL(2,Z).</h2>

<p>
    1.1</p>

<p>
    26 November 2022
  </p>

</div>
<p><b>
    Siu-Hung Ng




  </b>
<br />Email: <span class="URL"><a href="mailto:rng@math.lsu.edu">rng@math.lsu.edu</a></span>
<br />Homepage: <span class="URL"><a href="https://www.math.lsu.edu/~rng/">https://www.math.lsu.edu/~rng/</a></span>
<br />Address: <br />Louisiana State University, Baton Rouge, LA, 70803, USA<br />
</p><p><b>
    Yilong Wang




  </b>
<br />Email: <span class="URL"><a href="mailto:wyl@bimsa.cn">wyl@bimsa.cn</a></span>
<br />Homepage: <span class="URL"><a href="https://yilongwang11.github.io">https://yilongwang11.github.io</a></span>
<br />Address: <br />Louisiana State University, Baton Rouge, LA, 70803, USA <br /> Current: Beijing Institute of Mathematical Sciences and Applications (BIMSA), Huairou, Beijing, China<br />
</p><p><b>
    Samuel Wilson




  </b>
<br />Email: <span class="URL"><a href="mailto:swil311@lsu.edu">swil311@lsu.edu</a></span>
<br />Homepage: <span class="URL"><a href="https://snw-0.github.io">https://snw-0.github.io</a></span>
<br />Address: <br />Louisiana State University, Baton Rouge, LA, 70803, USA<br />
</p>

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<h3>Copyright</h3>
<p>© 2022 by Siu-Hung Ng, Yilong Wang, and Samuel Wilson</p>

<p>This package is free software; you can redistribute it and/or modify it under the terms of the <span class="URL"><a href="https://www.fsf.org/licenses/gpl.html">GNU General Public License</a></span> as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.</p>

<p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA"></a></p>
<h3>Acknowledgements</h3>
<p>This project is partially supported by NSF grant DMS 1664418.</p>

<p><a id="X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8"></a></p>

<div class="contents">
<h3>Contents<a id="contents" name="contents"></a></h3>

<div class="ContChap"><a href="chap1_mj.html#X7DFB63A97E67C0A1">1 <span class="Heading">Introduction</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X8360C04082558A12">1.1 <span class="Heading">Installation</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X86A9B6F87E619FFF">1.2 <span class="Heading">Usage</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap2_mj.html#X7BBCB13F82ACC213">2 <span class="Heading">Description</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X7F6278CD87400D49">2.1 <span class="Heading">Construction</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X86466B2786DD47C4">2.1-1 <span class="Heading">Weil representations</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7A8505DA8318656E">2.1-2 <span class="Heading">Character subspaces and primitive characters</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X85605F1983AA938D">2.1-3 <span class="Heading">Irrep Types</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X785B74657C952121">2.1-4 <span class="Heading">S and T matrices</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X861BA4A8800E1A08">2.2 <span class="Heading">Weil representation types</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7AEC048F793F1D79">2.2-1 <span class="Heading">Type D</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X84E15A1E8326AF4F">2.2-2 <span class="Heading">Type N</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7B788E2F87AF51CA">2.2-3 <span class="Heading">Type R, generic cases</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7B1E74AC85CBD40B">2.2-4 <span class="Heading">Type R, unary and extremal cases</span></a>
</span>
</div></div>
</div>
<div class="ContChap"><a href="chap3_mj.html#X7C4165447B8AB223">3 <span class="Heading">Irreducible representations of prime-power level</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X82DA126D7F755B1C">3.1 <span class="Heading">Representations of type D</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X845D92CB7841CB0B">3.1-1 SL2ModuleD</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7FDB517981A2C091">3.1-2 SL2IrrepD</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7CD74CFC84B38042">3.2 <span class="Heading">Representations of type N</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7A50CC5A7933E207">3.2-1 SL2ModuleN</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X81D60FE878F02838">3.2-2 SL2IrrepN</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7D9759387C499FA0">3.3 <span class="Heading">Representations of type R</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7B10D99E7AEAC411">3.3-1 SL2ModuleR</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X80961A2C7C5F632E">3.3-2 SL2IrrepR</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7C94E3007A1BEE85">3.3-3 SL2IrrepRUnary</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap4_mj.html#X8168FF017B2C0BB2">4 <span class="Heading">Lists of representations</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X80406B597E11D7C6">4.1 <span class="Heading">Lists by degree</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7CC7D26D7E37A1B9">4.1-1 SL2IrrepsOfDegree</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X7D5FF1AE85318A70">4.1-2 SL2IrrepsOfMaxDegree</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X78C583957D3FF6ED">4.2 <span class="Heading">Lists by level</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X8209AFA6825C44DC">4.2-1 SL2IrrepsOfLevel</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4_mj.html#X80400C6D79D4D0D6">4.3 <span class="Heading">Lists of exceptional representations</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4_mj.html#X87A4E88F784B5B9A">4.3-1 SL2IrrepsExceptional</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chap5_mj.html#X794C1A137F8FA14D">5 <span class="Heading">Methods for testing</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap5_mj.html#X7DE7E7187BE24368">5.1 <span class="Heading">Testing</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X801680187A8CA462">5.1-1 SL2WithConjClasses</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7A97C7C77C7608D0">5.1-2 SL2ChiST</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7BFA24298556FF78">5.1-3 SL2TestPositions</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap5_mj.html#X7B41A0178465F138">5.1-4 SL2TestSymmetry</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chapBib_mj.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd_mj.html"><span class="Heading">Index</span></a></div>
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