Mathematics Colloquia and Seminars
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k-Schur functions, Macdonald polynomials, and quantum cohomologyAlgebra & Discrete Mathematics
|Speaker: ||Jennifer Morse, University of Miami|
|Location: ||1147 MSB|
|Start time: ||Thu, Jan 12 2006, 12:10PM|
The k-Schur functions arose in our study of an open problem on
Macdonald polynomials, and were conjectured to satisfy properties
that refine classical ideas in symmetric function theory such as
Pieri rules, Kostka numbers, the Young lattice and Young tableaux.
We have recently proven these conjectures, illustrating that the
k-Schur functions refine the Schur functions in a combinatorial sense.
More generally, we have discovered that the k-Schur functions also
play a geometric role that mimics the Schur function role in the
cohomology of the Grassmannian. It turns out that the k-Schur functions
are connected to quantum cohomology, and their Littlewood-Richardson
coefficients are 3-point Gromov-Witten invariants. This leads to a
new approach to the open problem of finding a combinatorial interpretation
for these constants. This is joint work with Luc Lapointe.