Rimányi–Tarasov–Varchenko's Wronskian presentation conjecture for quantum K-theory of partial flags

Let Fl=Fl(v1,,vk;N)Fl=Fl(v_1,\dots,v_k;N) be a partial flag variety, let WQW_Q be the discrete Wronskian matrix appearing in the Bethe-algebra description, and let QK(Fl)QK(Fl) denote its quantum KK-ring. Rimányi–Tarasov–Varchenko's Wronskian presentation conjecture. The quantum KK-ring has a presentation determined by the determinant of WQW_Q.

QK(Fl) has a presentation given by det(WQ).QK(Fl)\text{ has a presentation given by }\det(W_Q).

The claim is the compact-limit prediction associated with the Bethe algebra; the source does not establish it in general, though it reports verification in the full-flag case through a quasimap theory.

Sources & referencesView supporting material

Primary source

Irit Huq-Kuruvilla, “Quantum K-Rings of Partial Flag Varieties, Coulomb Branches, and the Bethe Ansatz”, arXiv:2409.15575 (2025).

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