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Speaker: Saúl Blanco, Cornell University
The Bruhat interval [u,v] is endowed with rich topological and combinatorial structure; for instance, it is Gorenstein*. On the other hand, not much is known of the remaining uv paths in the Bruhat graph B(u,v) of [u,v]. Consider the poset SP(u,v) of shortest uv paths in B(u,v). SP(u,v) and [u,v] have similarities; for example, if there is only one rising chain (using the reflection order) in SP (u, v), then SP (u, v)) is also a Gorenstein*. Further properties of SP (u, v) will be discussed.