Category {\mathscr{C}}_{k} of multi-loop algebra representations versus modular representations: Questions of G. Lusztig.

Lusztig defined an abelian category {\mathscr {C}}_{k} of a class of representations of a multi-loop algebra and asked various questions connecting it to the modular representation theory of simple algebraic groups in char. p>0. The aim of this paper is to show that some of these questions have negative answer. [ABSTRACT FROM AUTHOR]