# The symmetric functions catalog

An overview of symmetric functions and related topics

2019-07-22

## Generalized Demazure atoms

The family of polynomials referred to as generalized Demazure atoms were introduced in [HMR12] and further studied in [TR13].

The generalized Demazure atoms are related to the fillings in the combinatorial model for non-symmetric Macdonald polynomials, [HHL08] and permuted-basement Macdonald polynomials, [Ale19a], but the definitions differ. The families studied in [Ale19a] and [AS19a] are referred to as permuted-basement atoms and are not the same as generalized Demazure atoms.

The generalized Demazure atoms have nice properties with respect to insertion algorithms and RSK, while the permuted-basement atoms are compatible with Demzure–Luzstig operators and representation theory.