A q-Analog of Foulke's conjecture
Abstract
We propose a q-analog of classical plethystic conjectures due to Foulkes. In our conjectures, a divided difference of plethysms of Hall-Littlewood polynomials Hn(x;q) replaces the analogous difference of plethysms of complete homogeneous symmetric functions hn(x) in Foulkes conjecture. At q=0, we get back the original statement of Foulkes, and we show that our version holds at q=1. We discuss further supporting evidence, as well as various generalizations.
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