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On plethysms and Sylow branching coefficients

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GR2W01 - Counting conjectures and beyond

We give a recursive formula for plethysm coefficients involved in Foulkes’ Conjecture, a long-standing open problem lying at the intersection of the theory of symmetric functions, the representation theory of symmetric groups and algebraic combinatorics. From this we deduce a stability result and resolve two conjectures of de Boeck concerning plethysms. We also obtain new results on Sylow branching coefficients for symmetric groups for the prime 2, the divisibility properties of which were recently used to characterise whether a Sylow subgroup of a finite group is normal and confirm a prediction of Malle and Navarro. This is joint work with Y. Okitani.

This talk is part of the Isaac Newton Institute Seminar Series series.

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