Jeremie Guilhot

Admissible subsets and Littelmann paths in affine Kazhdan-Lusztig theory

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 W0. The set of Weyl characters sλ forms a basis of the center and Lusztig showed in [11] that these characters act as translations on the Kazhdan–Lusztig basis element Cw0

Kazhdan-Lusztig Cells in Affine Weyl Groups of Rank 2

{C}_{w_0}

GENERALIZED INDUCTION OF KAZHDAN-LUSZTIG CELLS

where w0 is the longest element of W0, that is, we have Cw0sλ=Cw0tλ

Cellularity of the lowest two-sided ideal of an affine Hecke algebra

{C}_{w_0}{\mathrm{s}}_{\uplambda}={C}_{w_0{t}_{\uplambda}}

Kazhdan-Lusztig cells in affine Weyl groups with unequal parameters

. As a consequence, the coefficients that appear when decomposing Cw0tλsτ