Quasisymmetric harmonics of the exterior algebra

The left regular representation of the symmetric group has a graded cousin constructed as a coinvariant quotient of the polynomial ring in n variables. This theory has fruitfully produced many interesting generalizations with a rich interplay between algebra and combinatorics. Examples include the famous diagonal harmonics and, slightly more recently, the Delta conjecture. In this talk, we review some relevant background and introduce a Grassmannian version of the coinvariant space using the Hivert action of the symmetric group. This is joint work with Nantel Bergeron, Farhad Soltani, and Mike Zabrocki.