These are some notes for Math 261a on topics that either weren't
treated in [Fulton and Harris], or the treatment there required stuff
we'd skipped. They're each about six pages.

<menu>
<li>Using rep theory of S_4 to describe a bouncing tetrahedron,
<a href="tetrahedron.ps">PostScript</a> and 
<a href="tetrahedron.pdf">PDF</a>

<li>Character theory for finite groups,
<a href="characters.ps">PostScript</a> and 
<a href="characters.pdf">PDF</a>

<li>Classification of U(n)'s irreps using the nonstandard notion
of "strong dominance"
<a href="UnReps.ps">PostScript</a> and 
<a href="UnReps.pdf">PDF</a>

<li>Barely enough algebraic geometry to appreciate the algebro-geometric
classification of irreps of GL_n,
<a href="BorelWeil.ps">PostScript</a> and 
<a href="BorelWeil.pdf">PDF</a>

<li>The dense orbit of N on GL_n/B, and applications,
<a href="Norbits.ps">PostScript</a> and 
<a href="Norbits.pdf">PDF</a>

<li>The Weyl character formula for GL_n, and the Gel'fand-Cetlin basis,
<a href="WCFandGC.ps">PostScript</a> and 
<a href="WCFandGC.pdf">PDF</a>

<li>The hive ring computes tensor products of GL_n reps,
<a href="hives.ps">PostScript</a> and 
<a href="hives.pdf">PDF</a>

<li>Each compact group gives a root system,
<a href="root1.ps">PostScript</a> and 
<a href="root1.pdf">PDF</a>
</menu>


<hr>
    This material is based upon work supported by the National
    Science Foundation under Grant No. 0072667.

<p>
    Any opinions, findings and conclusions or recomendations
    expressed in this material are those of the author and do not
    necessarily reflect the views of the National Science Foundation.