Representation Theory, Math 9140b, Winter 2010

Presentations

All students must attend all of the presentations.

Possible topics. Some of these refer to sections of Sternberg's book Group Theory and Physics. Additional topics may be added later depending on where we get to in the course. You may also suggest completely different topics. You should choose a topic that is not something you already know about.

• the Murnaghan-Nakayama rule, giving a formula for the irreducible characters of S_n (see Fulton, Young Tableaux, or James-Kerber, The representation theory of the symmetric group)
• the Littlewood-Richardson rule describing the multiplicity of an irrep of S_n in a tensor product of such irreps (see James-Kerber, The representation theory of the symmetric group)
• the Robinson-Schensted-Knuth correspondence (see Fulton, Young Tableaux, chapter 4)
• representations of semidirect products of groups (3.8 in Sternberg, but I believe there are slicker ways to do it; ask me for references)
• representations of Lie algebras (4.10) and su(2) (4.11)
• representations of quantum groups, or just SL_q(2) (ask me for references)
• modular representation theory, i.e. representations over finite fields; maybe also the stable module category of a group (ask me for references)
• applications to particle physics (3.9, 3.10, 3.12, 5.9 to 5.12, ...)
• applications to crystalography (1.5, 1.8, 1.9, 1.10)
• other applications (4.5 to 4.9)

Timeline:

• Choose your date by Feb 25
• Meet with me to discuss topics.
• Choose your topic ≥ 4 weeks ahead of your date.
• Give me an outline (~1 page) ≥ 3 weeks ahead of your date.
• Give me a draft of the talk ≥ 2 weeks ahead of your date.

The presentation is worth 30% of the final grade. Grade based on:

• knowledge of the material
• organization of material (what you choose to cover and how you choose to organize it)
• clarity of presentation (how you present it: choice of notation, speak clearly, face the audience, etc)
• blackboard use (use boards in order, don't erase what you just wrote, don't stand in front of what you write, etc)
• timing (45-55 min gets full marks, too short or too long gets reduced marks; you might consider building in some flexibility at the end of the talk)

You should use the blackboard, and you should practice the talk at least once or twice beforehand, on a blackboard with someone listening. And you should time the practice talks.