Crystals from KLR and preprojective algebras
Last update: 11 October 2012
a complex reductive algebraic group corresponds to
Let be a fundamental region for the action of on
Make a graph with vertices and
The quiver Hecke algebra:
Choose an orientation.
The quiver Hecke algebra has generators
and more... where
(generating function in noncommutative
As directed graphs with labels
Idea: Replace beads by vector spaces.
The data of
- a vector space for each vertex
- a linear transformation for each edge
is a representation of (or
In the case of require
and we require
As discrete graphs with labels
Notes and References
These are a typed version of lecture notes for the fifth in a series of lectures given at the Brazil Algebra Conference, Salvador, 19 July 2012.