3:00 p.m., Friday (September 15, 2006)

MATX 1100

Steph van Willigenburg

A combinatorial classification of skew Schur functions

Littlewood-Richardson coefficients arise in a number of areas including algebraic geometry, algebra, and representation theory. However, computing them is #P-complete. One way to reduce the number of coefficients needed to be computed is to find classes of coefficients that are equal. In this talk we investigate the question of Littlewood-Richardson coefficient equality via the study of skew Schur function equality.

More precisely, we define an equivalence relation on diagrams such that two diagrams are equivalent if and only if their corresponding skew Schur functions are equal. When the diagrams are of a certain type this reduces to an equivalence relation on integer compositions. We give a combinatorial interpretation of this integer composition relation and relate it to other known combinatorial objects. If time permits we will also discuss how the combinatorial interpretation can be generalised.

No prior knowledge of any of the above is required.

Refreshments will be served at 2:45 p.m. (Lounge, MATX 1115).

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