3094 — Course Outline

Warning: For schedule with due dates, please go to the schedule page.

Topics to be covered: Intro to proofs, linear algebra and group THeory, Coxeter groups, Bruhat order, weak order

J = Tom Judson’s Abstract Algebra: THeory and Applications (HTML and Sage exercises)
BB = Combinatorics of Coxeter Groups (Springer, 2005) by Anders Björner and Francesco Brenti
H = James E. Humphreys: Reflection Groups and Coxeter Groups.
J 1.1 Sets and equivalence relations
J 1.2 Review Induction and exercises
J 3.1 Integer equivalence classes and symmetries
J 3.2 groups and examples
J 3.3 subgroups
J 4.1 cyclic groups
J 5.1 Def of symmetric group, permutation group
J 5.2 Dihedral groups
J 9 Isomorphism? Direct product?
J 12.1, 12.2 Matrix groups and symmetry
J 20 Vector space and oTHer linear algebra basics
BB 1.1 Coxeter systems, relations, when are two words equivalent?
BB 1.2 Examples
BB 1.2 Reflection groups, finite and affine and hyperbolic?
BB 1.2 and H Weyl groups
BB 1.2 and H Weyl group examples
J 19.1-19.2, BB A2 posets, lattice, etc
BB 2.1 Bruhat order basics
BB 3.1 Weak order basics
J 10.1 quotient group
BB 1.1, DF 6.3 group presentation