Riordan trees and the homotopy sl_2 weight system - Archive ouverte HAL
Article Dans Une Revue Journal of Pure and Applied Algebra Année : 2017

Riordan trees and the homotopy sl_2 weight system

Résumé

The purpose of this paper is twofold. On one hand, we introduce a modification of the dual canonical basis for invariant tensors of the 3-dimensional irreducible representation of U_q(sl_2), given in terms of Jacobi diagrams, a central tool in quantum topology. On the other hand, we use this modified basis to study the so-called homotopy sl_2 weight system, which is its restriction to the space of Jacobi diagrams labeled by distinct integers. Noting that the sl_2 weight system is completely determined by its values on trees, we compute the image of the homotopy part on connected trees in all degrees; the kernel of this map is also discussed.
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Dates et versions

hal-01176858 , version 1 (16-07-2015)

Identifiants

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Jean-Baptiste Meilhan, Sakie Suzuki. Riordan trees and the homotopy sl_2 weight system. Journal of Pure and Applied Algebra, 2017, 221 (3), pp. 691-706. ⟨10.1016/j.jpaa.2016.07.012⟩. ⟨hal-01176858⟩
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