Date: Thursday, February 14, 2013
Location: 3096 East Hall (3:00 PM to 4:00 PM)
Title: Geometric Littlewood-Richardson rules
Abstract: The ring of symmetric functions is the cohomology ring of Grassmannians. The Schur functions $s_\lambda$ are a $\mathbb{Z}$-basis of it. These functions are indexed by partitions $\lambda$; the multiplicative structure of the ring is given by the Littlewood-Richardson coefficients appearing in $s_\lambda s_\mu = \sum c_{\lambda \mu}^\nu s_nu$. Vakil found a geometric way of determining the Littlewood-Richardson coefficients. Knutson generalized his method, thus also determining equivariant cohomology and $K$-theory of Grassmannians. We will study a deformation of the ring of symmetric functions which naturally appears in equivariant homology of Grassmannians. We will discuss a $\mathbb{Z}[t]$-basis of it, and sketch the way toward a Littlewood-Richardson rule for determining the ring structure. (Joint work with Allen Knutson.)
Speaker: Mathias Lederer
Institution: Universität Bielefeld
Event Organizer:
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