A Counterexample to a Conjecture on Fused Specht Polynomials

Darij Grinberg

A Counterexample to a Conjecture on Fused Specht Polynomials

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Contributed by Darij Grinberg ↗

Version 1 / Sep 28, 2026 / CC0 1.0

Abstract

Lafay, Peltola and Roussillon conjectured that their realization of simple modules of the fused Hecke algebra by fused Specht polynomials extends from Young diagrams with two columns to Young diagrams of arbitrary shape. We give a counterexample for \[ n=8,\qquad \lambda=(3,2,2,1),\qquad \varsigma=(2,2,2,2). \] More precisely, we exhibit an explicit linear dependence among three fused Specht polynomials indexed by row-strict Young tableaux. The same example also yields an infinite family of counterexamples.

Provenance statement

Produced by GPT-5.6 Sol. I have verified Section 1 using SageMath; thus the counterexample is definitely correct.

References

Augustin Lafay, Eveliina Peltola and Julien Roussillon, Fused Specht Polynomials and $c=1$ Degenerate Conformal Blocks , arXiv:2410.09798v3, 2025. https://arxiv.org/abs/2410.09798v3 .arXiv

Version history

v1Submitted by Darij GrinbergInitial depositCurrentSep 28, 2026