On multigraded generalizations of Kirillov-Reshetikhin modules

Bianchi, A., Chari, V., Fourier, G. and Moura, A. (2014) On multigraded generalizations of Kirillov-Reshetikhin modules. Algebras and Representation Theory, 17(2), pp. 519-538. (doi: 10.1007/s10468-013-9408-0)

Abstract

We study the category of Z-graded modules with finite-dimensional graded pieces for certain Z +-graded Lie algebras. We also consider certain Serre subcategories with finitely many isomorphism classes of simple objects. We construct projective resolutions for the simple modules in these categories and compute the Ext groups between simple modules. We show that the projective covers of the simple modules in these Serre subcategories can be regarded as multigraded generalizations of Kirillov–Reshetikhin modules and give a recursive formula for computing their graded characters.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Fourier, Dr Ghislain
• Authors: Bianchi, A., Chari, V., Fourier, G., and Moura, A.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Algebras and Representation Theory
• Publisher: Springer Verlag
• ISSN: 1386-923X
• ISSN (Online): 1572-9079