- Crystal structure of certain PBW bases
- 04/18/2018
- 4:10 PM - 5:00 PM
- C304 Wells Hall
- Ben Salisbury, Central Michigan University
Lusztig's theory of PBW bases gives a way to realize the crystal $B(\infty)$ for any complex-simple Lie algebra where the underlying set consists of Kostant partitions. In fact, there are many different such realizations: one for each reduced expression of the longest element of the Weyl group. There is an explicit algorithm to calculate the actions of the crystal operators, but it can be quite complicated. In this talk, we will explain how, for certain reduced expressions, the crystal operators can also be described by a much simpler bracketing rule. Conditions describing these reduced expressions will be given in every type except $E_8$, $F_4$ and $G_2$ and several examples will be provided. This is joint work with Jackson Criswell, Peter Tingley, and Adam Schultze.