Finite-Dimensional Representations of Hyper Loop Algebras Over Non-Algebraically Closed Fields

TL;DR

This paper classifies and constructs finite-dimensional representations of hyper loop algebras over non-algebraically closed fields, exploring their structure, tensor products, and connections to polynomial algebras and Galois theory.

Contribution

It provides a classification of irreducible representations, constructs Weyl modules, and analyzes the category structure over non-algebraically closed fields.

Findings

Classification of irreducible representations

Construction of Weyl modules

Analysis of tensor products and block decomposition

Abstract

We study finite-dimensional representations of hyper loop algebras over non-algebraically closed fields. The main results concern the classification of the irreducible representations, the construction of the Weyl modules, base change, tensor products of irreducible and Weyl modules, and the block decomposition of the underlying abelian category. Several results are interestingly related to the study of irreducible representations of polynomial algebras and Galois theory.