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The cohomology of the affine Grassmannian and a new combinatorial formula for fusion coefficients
Student-Run Combinatorics & Algebra| Speaker: | Anne Schilling, UC Davis |
| Location: | 1147 MSB |
| Start time: | Thu, Jan 26 2012, 1:10PM |
Description
It is a classical result of Schubert calculus that the intersection multiplicities
of certain Schubert varieties (Grassmannians) are intimately related to the Littlewood-Richardson
coefficients, which arise as structure coefficients of Schur functions.
This has recently been generalized to the affine setting by Lam, Lapointe, Morse, Shimozono
and others. In particular, the affine analogues of the Schur functions have structure
coefficients, which include fusion coefficients. It has been a notoriously difficult
problem to find a combinatorial (or positive) formula for these coefficients.
Here we combine algebraic geometry, representation theory, and combinatorics to give
a new combinatorial formula for the fusion coefficients in certain cases. This is
based on joint work with Jennifer Morse.