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 $W\_0$. The set of Weyl characters {\sf s}\_\la forms a basis of the center and Lusztig showed in [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

Kazhdan-Lusztig cells in the affine Weyl groups of rank 2

In this paper we determine the partition into Kazhdan-Lusztig cells of the affine Weyl groups of type \tB_{2} and \tG_{2} for any choice of parameters. Using these partitions we show that the semicontinuity conjecture of Bonnaf\'e holds for these groups.Comment: 21 pages, 4 tables, 13 figures. Section 3 has been completely rewritten. The new version also contains some minor correction

On the lowest two-sided cell in affine Weyl groups

Bremke and Xi determined the lowest two-sided cell for affine Weyl groups with unequal parameters and showed that it consists of at most |W_{0}| left cells where W_{0} is the associated finite Weyl group. We prove that this bound is exact. Previously, this was known in the equal parameter case and when the parameters were coming from a graph automorphism. Our argument uniformly works for any choice of parameters.Comment: 18 pages, 1 figure, final version (minor changes). To appear in Representation theor

On the determination of Kazhdan-Lusztig cells in affine Weyl groups with unequal parameters

Let W be a Coxeter group and L be a weight function on W. Following Lusztig, we have a corresponding decomposition of W into left cells, which have important applications in representation theory. We study the case where $W$ is an affine Weyl group of type $\tilde{G_{2}}$. Using explicit computation with \textsf{CHEVIE}, we show that (1) there are only finitely many possible decompositions into left cells and (2) the number of left cells is finite in each case, thus confirming some of Lusztig's conjectures in this case. For the proof, we show some equalities on the Kazhdan-Lusztig polynomials which hold for any affine Weyl groups.Comment: 22 pages, 2 figures, the revised version contains additional reference and some rewritting. Submitte

Assessing the impact of the main East-Asian free trade agreements using a gravity model. First results

The purpose of this article is to assess the impact of the three main East-Asian free trade agreements (ASEAN, ASEAN-China and ASEAN-South Korea) on intra-regional and extra- regional trade. To do this, we use a panel-data gravity model with three regional indicator variables. On the basis of the results, we conclude that the ASEAN agreement favours regional and multilateral trade, with the creation of exports to the rest of the world outweighing the diversion of extra-regional imports. The ASEAN-China and ASEAN-South Korea agreements have thus far not been shown to have an impact on East-Asian trade flows.Free Trade Agreement, East Asia, Gravity model

Affine cellularity of affine Hecke algebras of rank two

We show that affine Hecke algebras of rank two with generic parameters are affine cellular in the sense of Koenig-Xi.Comment: 24 pages, 4 figures and 14 tables. New version: added references, corrected typos. Final versio