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- W2885127560 abstract "How to study a nice function on the real line? The physically motivated Fourier theory technique of harmonic analysis is to expand the function in the basis of exponentials and study the meaningful terms in the expansion. Now, suppose the function lives on a finite non-commutative group G, and is invariant under conjugation. There is a well-known analog of Fourier analysis, using the irreducible characters of G. This can be applied to many functions that express interesting properties of G. To study these functions one wants to know how the different characters contribute to the sum? In this note we describe the $$G=SL_{2}({mathbb {F}}_{q})$$ case of the theory we have been developing in recent years which attempts to give a fairly general answer to the above question for finite classical groups. The irreducible representations of $$SL_{2}({mathbb {F}}_{q})$$ are “well known” for a very long time (Frobenius in Sitzber Preuss Akad Wiss 985–1021, 1896; Jordan in Am J Math 29:387–405, 1907; Schur in Journal für die reine und angewandte Mathematik 132:85–137, 1907) and are a prototype example in many introductory courses on the subject. We are happy that we can say something new about them. In particular, it turns out that the representations that were considered as “anomalous” in the “old” point of view (known as the “philosophy of cusp forms”) are the building blocks of the current approach." @default.
- W2885127560 created "2018-08-22" @default.
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- W2885127560 date "2018-08-16" @default.
- W2885127560 modified "2023-09-26" @default.
- W2885127560 title "A look at representations of $$SL_{2}({mathbb {F}}_{q})$$ S L 2 ( F q ) through the lens of size" @default.
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- W2885127560 doi "https://doi.org/10.1007/s40863-018-0098-8" @default.
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