Steinberg skein identities at roots of unity

Vijay Higgins; Indraneel Tambe

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arXiv · 2509.05502

Steinberg skein identities at roots of unity

Vijay Higgins·Indraneel Tambe

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Abstract

We obtain a family of skein identities in the Kauffman bracket skein module which relate Frobenius elements to Jones-Wenzl projectors at roots of unity. We view these skein identities as certain incarnations of Steinberg tensor product formulae from the theory of tilting modules of the quantum group $U_q(sl_2)$. We show that the simplest skein identities yield a short new proof of the existence of the Chebyshev-Frobenius homomorphism of Bonahon-Wong.

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BibTeX RIS

Vijay Higgins, Indraneel Tambe. 2025-09-05. Steinberg skein identities at roots of unity. https://arxiv.org/abs/2509.05502

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