Prove the six affine Jacobi–Trudi identities conjectured by Ole Warnaar for the relevant specialisations of multiparameter Hall–Littlewood polynomials of types B_n, C_n, and BC_n, for rectangular shapes. The supplied sources identify the family of identities and their polynomial types, but do not reproduce the six individual formulas or their complete parameter ranges.

Warnaar’s affine Jacobi–Trudi conjectures

Prove the six affine Jacobi–Trudi identities conjectured by Ole Warnaar for the relevant specialisations of multiparameter Hall–Littlewood polynomials of types $\mathrm{B}_n$ , $\mathrm{C}_n$ , and $\mathrm{BC}_n$ , for rectangular shapes. The supplied sources identify the family of identities and their polynomial types, but do not reproduce the six individual formulas or their complete parameter ranges.

References

Primary source

arXiv

Additional references

Character expansions and affine Jacobi-Trudi identities — arXiv — Ilse Fischer, Moritz Gangl, Álvaro Gutiérrez, Nishu Kumari

algebraic-combinatorics representation-theory symmetric-functions

Posted 18 hours ago · edited 18 hours ago

Progress summary

Refreshed 18 hours ago

Claimed solved

A new unrefereed preprint claims to prove all six identities, but that claim has not been independently checked.

Warnaar’s package concerns six affine Jacobi–Trudi identities for multiparameter Hall–Littlewood polynomials in types $\mathrm{B}_n$ , $\mathrm{C}_n$ , and $\mathrm{BC}_n$ . His 2026 paper presented these identities as conjectures, while proving a related affine formula for Schur functions.

Known results

Warnaar, 2026: proved an affine dual Jacobi–Trudi analogue for Schur functions indexed by rectangular partitions of arbitrary height; the Hall–Littlewood identities remained conjectural.

October 6, 2026 preprint

Ilse Fischer, Moritz Gangl, Álvaro Gutiérrez, and Nishu Kumari report that character expansions in types $\mathrm{B}$ , $\mathrm{C}$ , and $\mathrm{BC}$ establish all six conjectured identities. This is a claimed complete resolution in an unrefereed preprint, without independent mathematical assessment.

Current status (as of October 2026): The six identities are claimed proved by a new preprint, but the claim remains unverified; the earlier conjectural status is superseded only provisionally.

Sources

No solutions have been posted yet.