Type B web divided-power exchange relation conjecture

Let Xi(k)\mathsf{X}_i^{(k)} denote the nonclassical divided-power web at position ii in Web(so2n+1)\mathbf{Web}(\mathfrak{so}_{2n+1}), with 1kn1\leq k\leq n. Divided-power exchange relation conjecture. For 1a,b,cn1\leq a,b,c\leq n, there exist ξC(q)\xi\in\mathbb{C}(q) and integers 1a,b,cn1\leq a',b',c'\leq n such that

Xi(a)Xi±1(b)Xi(c)=ξXi±1(a)Xi(b)Xi±1(c)+LOTa,b,c,\mathsf{X}_i^{(a)}\mathsf{X}_{i\pm1}^{(b)}\mathsf{X}_i^{(c)}=\xi\,\mathsf{X}_{i\pm1}^{(a')}\mathsf{X}_i^{(b')}\mathsf{X}_{i\pm1}^{(c')}+\mathrm{LOT}_{a,b,c},

where LOTa,b,c\mathrm{LOT}_{a,b,c} is a linear combination of terms of the forms Xi(k)Xi±1()\mathsf{X}_i^{(k)}\mathsf{X}_{i\pm1}^{(\ell)} and Xi±1()Xi(k)\mathsf{X}_{i\pm1}^{(\ell)}\mathsf{X}_i^{(k)}. This conjectures further relations among nonclassical divided powers in type B webs, generalizing the cited iota-Serre relation; the coefficients and indices are not specified more precisely here, so deriving an explicit complete relation remains open.

Sources & referencesView supporting material

Primary source

Elijah Bodish, Ben Elias and David E. V. Rose, “Type B Webs”, arXiv:2607.13252 (2026).

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