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Math 6161- Algebraic Combinatorics :
Symmetric Functions |
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class day =
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midterm =
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final =
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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.
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May 6
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The Symmetric group, permutations, cycle
structure, matrix representations, G-modules, reducibility S1.1-1.3
Exercises : 1, 2
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May 8
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Complete reducibility and Maschke's theorem S1.4-1.5
Exercises: 3, 4
Maple Exercises: 1
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May 13
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Schur's Lemma, Commutant algebra S 1.6-1.7
Exercises: 5, 6, 7
Maple Exercises: 2, 3
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May 15
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Group Characters S 1.8-1.9
Exercises: 8, 9, 10, 11
Maple Exercises: 4, 5
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May 20
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Reynolds operators and decomposition of the group algebra S 1.10
Maple Exercises: 6
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May 22
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Restriction, induction and midterm EXAMple S 1.11-1.12
Exercises: finish the exam
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May 27
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Partitions and intro to symmetric functions, relation to
class functions of the symmetric group
Exercises: 1,2,3 on partitions
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May 29
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power, elementary, homogeneous basis, scalar product, product,
coproduct
Exercises: finish the exam
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June 3
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dual to product, inner product, symmetric polynomials
Exercises: 5, 6 scalar products
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June 5
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monomial basis, change of basis coefficients
Exercises: 7, 8, 9
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June 10
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Schur functions
Exercises: prove dim \chi^\mu = the number of std tableaux of shape \mu
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June 12
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final exam
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Exercises:
See the running list of homework problems on the handouts page.
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