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.
  • Using rep theory of S_4 to describe a bouncing tetrahedron, PostScript and PDF
  • Character theory for finite groups, PostScript and PDF
  • Classification of U(n)'s irreps using the nonstandard notion of "strong dominance" PostScript and PDF
  • Barely enough algebraic geometry to appreciate the algebro-geometric classification of irreps of GL_n, PostScript and PDF
  • The dense orbit of N on GL_n/B, and applications, PostScript and PDF
  • The Weyl character formula for GL_n, and the Gel'fand-Cetlin basis, PostScript and PDF
  • The hive ring computes tensor products of GL_n reps, PostScript and PDF
  • Each compact group gives a root system, PostScript and PDF

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

    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.