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Quantitative Equidistribution for Certain Quadruples in Quasi-Random Groups: Erratum

Published online by Cambridge University Press:  22 September 2015

TIM AUSTIN
TIM AUSTIN*
Affiliation:
Courant Institute, New York University, New York, NY 10012, USA (e-mail: tim@cims.nyu.edu)
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In my recent paper [1] there is a mistake in the proof of Corollary 3. The first line of the displayed equation in that proof asserts that

\[\int_G|\langle u,\pi^g v\rangle_V|^2\,\rm{d} g = \int_G\langle u\otimes u,(\pi^g\otimes \pi^g)(v\otimes v)\rangle_{V\otimes V}\, \rm{d} g.\]
However, since the paper uses complex-valued representations, the integrand on the right here may not retain the absolute value of that on the left. Without this equality, the proof of Corollary 3 can no longer be reduced to an application of Lemma 2. However, it can be proved directly from Schur Orthogonality along very similar lines to the proof of Lemma 2.

Type
Erratum
Information
Combinatorics, Probability and Computing , Volume 25 , Issue 3 , May 2016 , pp. 484 - 485
Copyright
Copyright © Cambridge University Press 2015 

References

[1] Austin, T. (2015) Quantitative equidistribution for certain quadruples in quasi-random groups. Combin. Probab. Comput. 24 376–381.CrossRefGoogle Scholar
[2] Bump, D. (2004) Lie Groups, Vol. 225 of Graduate Texts in Mathematics, Springer.CrossRefGoogle Scholar