Schedule

 Course Description Handouts Computer Labs Links Schedule References
 Math 6161- Algebraic Combinatorics : Symmetric Functions

 May/June S Su M Tu W Th F 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12 13

class day =

midterm =

final =

I will try to keep a diary/schedule of the topics we cover in the class and roughly the sections that they correspond to in the text. S = Segan the Symmetric Group, N = Class notes.
The "Labs" that are referred to below are just Maple worksheets which will have programs and examples which we discuss in class.  These can be found on the 'Computer Lab' page.

 May 6 The Symmetric group, permutations, cycle structure, matrix representations, G-modules, reducibility S1.1-1.3 Exercises : 1, 2 May 8 Complete reducibility and Maschke's theorem S1.4-1.5 Exercises: 3, 4 Maple Exercises: 1 May 13 Schur's Lemma, Commutant algebra S 1.6-1.7 Exercises: 5, 6, 7 Maple Exercises: 2, 3 May 15 Group Characters S 1.8-1.9 Exercises: 8, 9, 10, 11 Maple Exercises: 4, 5 May 20 Reynolds operators and decomposition of the group algebra S 1.10 Maple Exercises: 6 May 22 Restriction, induction and midterm EXAMple S 1.11-1.12 Exercises: finish the exam May 27 Partitions and intro to symmetric functions, relation to class functions of the symmetric group Exercises: 1,2,3 on partitions May 29 power, elementary, homogeneous basis, scalar product, product, coproduct Exercises: finish the exam June 3 dual to product, inner product, symmetric polynomials Exercises: 5, 6 scalar products June 5 monomial basis, change of basis coefficients Exercises: 7, 8, 9 June 10 Schur functions Exercises: prove dim \chi^\mu = the number of std tableaux of shape \mu June 12 final exam

Exercises:
See the running list of homework problems on the handouts page.