Gorsky–Oblomkov–Rasmussen algebraic and inductive filtration conjecture

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Let m,nm,n be coprime positive integers with m>nm>n, and let Lmn\mathrm{L}_{\frac{m}{n}} be the finite-dimensional irreducible representation of the rational Cherednik algebra Hmn\mathrm{H}_{\frac{m}{n}}. Equip it with the algebraic filtration FalgF^{\mathrm{alg}} and the inductive filtration FindF^{\mathrm{ind}}. Gorsky–Oblomkov–Rasmussen conjecture. On Lmn\mathrm{L}_{\frac{m}{n}}, the algebraic filtration coincides with the inductive filtration:

Falg=Find.F^{\mathrm{alg}}=F^{\mathrm{ind}}.

The conjecture concerns the compatibility of two filtrations on rational Cherednik representations; the supplied text gives no resolution status.

References

Primary source

Xinchun Ma, “Rational Cherednik Algebras and Torus Knot Invariants”, arXiv:2402.18770 (2024).

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