Abstract
N. Katz has shown that any irreducible representation of the Galois group of \({\mathbb{F}}_{q}((t))\) 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.
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References
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The author acknowledges the support of the European Research Council during the preparation of this paper.
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Dedicated to the memory of Leon Ehrenpreis
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Kazhdan, D. (2013). On a Theorem of N. Katz and Bases in Irreducible Representations. In: Farkas, H., Gunning, R., Knopp, M., Taylor, B. (eds) From Fourier Analysis and Number Theory to Radon Transforms and Geometry. Developments in Mathematics, vol 28. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4075-8_15
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DOI: https://doi.org/10.1007/978-1-4614-4075-8_15
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