Factorization of the canonical bases for higher level Fock spaces

Susumu Ariki (1) , Nicolas Jacon (2) , Cédric Lecouvey (3)

1 RIMS - Research Institute for Mathematical Sciences
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
3 LMPT - Laboratoire de Mathématiques et Physique Théorique

The level l Fock space admits canonical bases G_e and G_\infty. They correspond to U_{v}(hat{sl}_{e}) and U_{v}(sl_{\infty})-module structures. We establish that the transition matrices relating these two bases are unitriangular with coefficients in N[v]. Restriction to the highest weight modules generated by the empty l-partition then gives a natural quantization of a theorem by Geck and Rouquier on the factorization of decomposition matrices which are associated to Ariki-Koike algebras.

Mots clés: decomposition matrix; canonical basis; Hecke algebra; Schur algebras; decomposition matrix.

Domaines: Théorie des représentations [math.RT]

Susumu Ariki, Nicolas Jacon, Cédric Lecouvey. Factorization of the canonical bases for higher level Fock spaces. Proceedings of the Edinburgh Mathematical Society, 2012, 55, pp.23-51. ⟨10.1017/S0013091510000519⟩. ⟨hal-00417495v4⟩