The set of nilpotent elements in a Lie algebra forms a normal, singular variety.  Springer gave a resolution of this “nilpotent cone” in 1969, and the fibers of this resolution have been studied since; for example, these “Springer fibers” can be used to give a construction of Specht modules.

 

Classically, the components of Springer fibers are indexed by standard Young tableaux, but in this talk, we will see why “webs” may be a better indexing set.  Webs arose to give a diagrammatic calculus for invariants in the representation theory of quantum groups, and you have probably encountered them before: the sl_2 (basis) webs coincide with noncrossing perfect matchings. In this talk, we will discuss two column Springer fibers, where we will see the web-based characterization and description of the smooth components are clearer than the equivalent tableaux-based descriptions, what we can do with this, and where we can go from here.

 

Faculty Host: Martha Precup