Abstract
The purpose of this paper is to present conjectures that extend to any “triangular” partitions (partitions “under any line” in the terminology of Blasiak-Haiman-Morse-Pun-Seelinger), properties of the Frobenius transform of multivariate diagonal harmonics modules. In their simplest version, these last modules correspond to the special case of “staircase” partitions, that is of the form ( n − 1 , n − 2 , … , 1 ) . The conjectures are motivated and supported both by extensive experimental computer algebra calculations, as well as stability properties.
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