Equivariant gamma-positivity conjecture for matroid Chow rings

Let MM be a loopless matroid of rank rr, let GG be a group of automorphisms of MM, and let

A(M)C=i=0r1ACiA(M)_{\mathbb{C}}=\bigoplus_{i=0}^{r-1}A^i_{\mathbb{C}}

be its complexified matroid Chow ring, with each graded piece carrying the induced CG\mathbb{C}G-module structure. Equivariant gamma-positivity conjecture. The ring A(M)CA(M)_{\mathbb{C}} is GG-equivariantly γ\gamma-positive, namely its equivariant Hilbert series admits a γ\gamma-expansion whose coefficients are classes of genuine complex representations of GG. This is the formal version of the equivariant conjecture attributed to Angarone, Nathanson, and Reiner; the source does not state that it has been resolved.

Sources & referencesView supporting material

Primary source

Hsin-Chieh Liao, “Equivariant gamma-positivity of matroid Chow rings”, arXiv:2408.00745 (2026).

Additional references

3 papers in this index state this conjecture (2008–2024). The statement above is taken from the most recent of them; the others are arXiv:2309.14312, arXiv:0801.2776.

Progress summary

Never refreshed

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

Solutions 0

No solutions have been posted yet.