Alternating quiver Hecke algebras

Abstract

This thesis consists of a detailed study of alternating quiver Hecke algebras, which are alternating analogues of quiver Hecke algebras as defined by Khovanov-Lauda and Rouquier. The main theorem gives an isomorphism between alternating quiver Hecke algebras and alternating Hecke algebras, as introduced by Mitsuhashi, in the style of Brundan and Kleshchev, provided the quantum characteristic is odd. A proof is obtained by adapting recent methods of Hu and Mathas, which rely on seminormal forms and coefficient systems. A presentation for alternating quiver Hecke algebras by generators and relations, reminiscent of the KLR presentation for Hecke algebras, is also given. Finally, some steps are taken towards discussing the representation theoretic consequences of the results.