07-1352/Class Notes for March 27

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Today's Agenda.

  • Decisions regarding student presentations.
  • PBW for {\mathcal A}(\uparrow).
  • PBW for {\mathcal A}(\uparrow_n).
  • The VS structure on {\mathcal A}(\uparrow_\star) and on {\mathcal B}_\star.
  • The algebra structure on {\mathcal A} and {\mathcal B}.
  • The graded representations {\mathcal E}_k and their decompositions into irreducibles:
  • Coloured stickers and tensor products over S_k.
  • Computing the homology.