Geodesic
The density of representation degrees
Journal of the European Mathematical Society, Tome 14 (2012) no. 5, pp. 1519-1537 Cet article a éte moissonné depuis la source EMS Press

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For a group G and a positive real number x, define dG​(x) to be the number of integers less than x which are dimensions of irreducible complex representations of G. We study the asymptotics of dG​(x) for algebraic groups, arithmetic groups and finitely generated linear groups. In particular we prove an "alternative" for finitely generated linear groups G in characteristic zero, showing that either there exists α>0 such that dG​(x)>xα for all large x, or G is virtually abelian (in which case dG​(x) is bounded).
DOI : 10.4171/jems/339
Classification : 20-XX, 00-XX 
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     author = {Martin W. Liebeck and Dan Segal and Aner Shalev},
     title = {The density of representation degrees},
     journal = {Journal of the European Mathematical Society},
     pages = {1519--1537},
     year = {2012},
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     number = {5},
     doi = {10.4171/jems/339},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/339/}
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Martin W. Liebeck; Dan Segal; Aner Shalev. The density of representation degrees. Journal of the European Mathematical Society, Tome 14 (2012) no. 5, pp. 1519-1537. doi: 10.4171/jems/339

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