Superspace quasisymmetric harmonics

Farhad Soltani (York university)

The quasisymmetrics in superspace are the invariants under hivert action when acting diagonally on commuting and anticommuting variables. By equipping the superspace with a bilinear form using partial derivative operators, the harmonics are the orthogonal complement of the ideal generated by nontrivial quasisymmetrics. The harmonics of the polynomial ring in commuting variables was counted by catalan numbers and then a basis indexed by “indexed forests” was given. An indexed forest is a sequence of binary rooted trees where the leaves form a noncrossing and nonnested partition.

I will speak about the harmonics of the superspace and we will see they are indexed by marked binary rooted trees in which the set of leaves form a noncrossing partition.

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