On a Theorem of N. Katz and bases in irreducible representations

Abstract

N. Katz has shown that any irreducible representation of the Galois group of Fq((t)) has unique extension to a special representation of the Galois group of k (t) unramified outside 0 and ∞ and tamely ramified at ∞. In this chapter, we analyze the number of not necessarily special such extensions and relate this question to a description of bases in irreducible representations of multiplicative groups of division algebras © Springer Science+Business Media New York 2013.