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Article Dans Une Revue Transformation Groups Année : 2018

Admissible subsets and Littelmann paths in affine Kazhdan-Lusztig theory

Jérémie Guilhot

Résumé

The center of an extended affine Hecke algebra is known to be isomorphic to the ring of symmetric functions associated to the underlying finite Weyl group $W_0$. The set of Weyl characters ${\sf s}_\la$ forms a basis of the center and Lusztig showed in~\cite{Lus15} that these characters act as translations on the Kazhdan-Lusztig basis element $C_{w_0}$ where $w_0$ is the longest element of $W_0$, that is we have $C_{w_0}{\sf s}_\la =C_{w_0t_\la}$. As a consequence, the coefficients that appear when decomposing~$C_{w_0t_{\la}}{\sf s}_\tau$ in the Kazhdan-Lusztig basis are tensor multiplicities of the Lie algebra with Weyl group $W_0$. The aim of this paper is to explain how admissible subsets and Littelmann paths, which are models to compute such multiplicities, naturally appear when working out this decomposition.
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Dates et versions

hal-01333423 , version 1 (17-06-2016)
hal-01333423 , version 2 (15-08-2018)

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Jérémie Guilhot. Admissible subsets and Littelmann paths in affine Kazhdan-Lusztig theory. Transformation Groups, 2018, 23 (4), pp.915-938. ⟨10.1007/s00031-018-9495-4⟩. ⟨hal-01333423v2⟩
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