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arXiv · 2505.07097

Compatibility of Higher Specht Polynomials and Decompositions of Representations

Shaul Zemel
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Abstract

%We show how to normalize the higher Specht polynomials of Ariki, Terasoma, and Yamada in a compatible way in order to define a stable version of these polynomials. We also decompose the non-transitive actions of Haglund, Rhoades, and Shimozono into orbits, and show how the associated basis of higher Specht polynomials of Gillespie and Rhoades respects that decomposition. For a given $n$, the orbits of the action of $S_{n}$ are associated with subsets of the set of positive integers that are smaller than $n$, and we relate the representation associated with a set $I$ to the ones of $S_{n+1}$ associated with $I$ and with its union with $n$, the latter being a lifting of the Branching Rule.

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Shaul Zemel. 2025-05-11. Compatibility of Higher Specht Polynomials and Decompositions of Representations. https://arxiv.org/abs/2505.07097

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