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