Complete flagged homogeneous polynomials
Abstract
We introduce a new basis for the polynomial ring which lifts the complete homogeneous symmetric polynomials while retaining representation theoretic significance. Using a specialized RSK algorithm we give an explicit nonnegative expansion into key polynomials and, generalizing the special rim hook tabloids of Egecioglu and Remmel, give an explicit signed expansion for key polynomials into this new basis.
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