Zabrocki's Frobenius-characteristic conjecture for the super-diagonal coinvariant ring

From papers

Let n1n\geq1. Let SDRn\operatorname{SDR}_n be the super-diagonal coinvariant ring in commuting variables x1,,xnx_1,\ldots,x_n, y1,,yny_1,\ldots,y_n and Grassmann variables θ1,,θn\theta_1,\ldots,\theta_n, with the symmetric group acting diagonally. Associate the θ\theta-degree with the parameter zz, and let Frob(SDRn;q,t,z)\operatorname{Frob}(\operatorname{SDR}_n;q,t,z) denote its graded Frobenius characteristic. Zabrocki's conjecture.

Frob(SDRn;q,t,z)=k=0nzkΔenk1en.\operatorname{Frob}(\operatorname{SDR}_n;q,t,z)=\sum_{k=0}^{n}z^k\Delta'_{e_{n-k-1}}e_n.

The conjecture gives a representation-theoretic interpretation of the symmetric functions in the Delta Conjecture. Its status is not resolved in the supplied text.

Progress summary

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Sources & referencesView supporting material

Primary source

James Haglund and Emily Sergel, “Schedules and the Delta Conjecture”, arXiv:1908.04732 (2020).

Solutions 0

No solutions have been posted yet.