On multigraded generalizations of Kirillov-Reshetikhin modules

TL;DR

This paper explores multigraded generalizations of Kirillov-Reshetikhin modules within certain graded Lie algebra categories, providing projective resolutions, Ext group computations, and recursive formulas for graded characters.

Contribution

It introduces multigraded Kirillov-Reshetikhin modules as projective covers and develops methods to compute their characters recursively.

Findings

Constructed projective resolutions for simple modules.

Computed Ext groups between simple modules.

Derived recursive formulas for graded characters.

Abstract

We study the category of Z^l-graded modules with finite-dimensional graded pieces for certain Z+^l-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.