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• W2963675782 abstract "Let π be a finite dimensional unitary representation of a group G with a generating symmetric n-element set S⊂G. Fix ε>0. Assume that the spectrum of |S| -1 ∑ s∈S π(s)⊗π(s) ¯ is included in [-1,1-ε] (so there is a spectral gap ≥ε). Let r N ' (π) be the number of distinct irreducible representations of dimension ≤N that appear in π. Then let R n,ε ' (N)=supr N ' (π) where the supremum runs over all π with n,ε fixed. We prove that there are positive constants δ ε and c ε such that, for all sufficiently large integer n (i.e. n≥n 0 with n 0 depending on ε) and for all N≥1, we have expδ ε nN 2 ≤R n,ε ' (N)≤expc ε nN 2 . The same bounds hold if, in r N ' (π), we count only the number of distinct irreducible representations of dimension exactly =N." @default.
• W2963675782 created "2019-07-30" @default.
• W2963675782 creator A5035197493 @default.
• W2963675782 date "2017-01-01" @default.
• W2963675782 modified "2023-09-30" @default.
• W2963675782 title "Quantum expanders and growth of group representations" @default.
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• W2963675782 doi "https://doi.org/10.5802/afst.1541" @default.
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