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Equivariant quasisymmetry and noncrossing partitions
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abstract
We introduce a definition of ``equivariant quasisymmetry'' for polynomials in two sets of variables. Using this definition we define quasisymmetric generalizations of the theory of double Schur and double Schubert polynomials that we call double fundamental polynomials and double forest polynomials, where the subset of ``noncrossing partitions'' plays the role of $S_n$. In subsequent work we will show this combinatorics is governed by a new geometric construction we call the ``quasisymmetric flag variety'' which plays the same role for equivariant quasisymmetry as the usual flag variety plays in the classical story.
Forward citations
Cited by 2 Pith papers
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The Springer Geometry of Specht Polynomials and Schubert cycle positivity for two row Springer fiber components
Two-row Springer fiber components have positive Schubert cycle expansions counted by reduced words compatible with noncrossing matchings.
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Richardson tableaux and Schubert positivity
The Schubert cycle expansion of a Springer fiber component equal to a Richardson variety, indexed by a Richardson tableau, is computed combinatorially using translation-equivalent Bruhat intervals and Sottile's Pieri rule.
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