
Matthew Dyer
University of Notre Dame
Shellability and highest weight representations
Friday 4th, April 12:0512:55pm,
Stephen Roberts.
Shellable simplicial complexes are built from the
empty complex by adding in the closures of the maximal faces
one at a time in a recursively controlled way; for such a complex, one
obtains detailed explicit information about the homotopy type,
cohomology etc. In this talk, a definition and some consequences of
an analogous notion of shellability of highest weight representation
categories will be described. For a special class of representation categories
associated to a pure simplicial complex, this notion reduces
to the shellability of the complex. It is expected that many natural
categories arising in Lie theory (e.g. category O of representations
of a semisimple complex Lie algebra or associated quantized
enveloping algebra) come from shellable ones; if true
this would provide a deeper, uniform explanation and stronger versions of
several important known common properties of these categories, such as factorizations of Shapovalov determinants.







