ON COMBINATORICS OF EXTENDED AFFINE ROOT SYSTEMS (TYPE A1) Attention - heure inhabituelle!

par Zahra Kharaghani (University of Isfahan et ICJ)

jeudi 15 juin 2017, 15:30 → 16:30 Europe/Paris

112 (bât. Braconnier)

We establish extensions of some important features of affine theory to A1-type affine reflection systems (extended affine root systems). We present a positivity theory which decomposes in a natural way the non-isotropic roots into positive and negative roots, give an extended version of the well-known exchange condition for the corresponding Weyl group, and finally give an extended version of the Bruhat ordering and the Z-Lemma. Furthermore, a new presentation of the Weyl group in terms of the parity permutations is given, this in turn leads to a parity theorem which gives a characterization of the reduced words in the Weyl group. All root systems involved in this work appear as the root systems of certain well studied Lie algebras.