|Date: Friday, October 23, 2015
Location: 4088 East Hall (3:10 PM to 4:00 PM)
Title: Crystal combinatorics from PBW bases
Abstract: We re-examine Lusztig's original construction of canonical bases in finite type. This construction starts by using the braid group action to construct PBW bases, and is fairly elementary. However, some of the remarkable properties of the canonical basis are already readily visible: most remarkably, the fact that it descends to a basis of every finite dimensional simple module. We describe how this leads to an alternative construction of Kashiwara's crystals, and to discuss the resulting combinatorics. In type A we recover familiar structures. In some other types, including type D, the combinatorics seems to be new, or at least not well known. Those parts of this work which are not due to Lusztig are joint with John Claxton, Ben Salisbury and Adam Schultze.
Speaker: Peter Tingley
Institution: Loyola U. Chicago