On the sharpness of the bound for the Local Converse Theorem of p-adic GLprime

Adrian, Moshe, Liu, Baiying, Stevens, Shaun and Tam, Geo Kam-Fai (2018) On the sharpness of the bound for the Local Converse Theorem of p-adic GLprime. Proceedings of the American Mathematical Society, Series B, 5. pp. 6-17. ISSN 2330-1511

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We introduce a novel ultrametric on the set of equivalence classes of cuspidal irreducible representations of a general linear group GL(N) over a nonarchimedean local field, based on distinguishability by twisted gamma factors. In the case that N is prime and the residual characteristic is greater than or equal to N/2, we prove that, for any natural number i at most N/2, there are pairs of cuspidal irreducible representations whose logarithmic distance in this ultrametric is precisely i. This implies that, under the same conditions on N, the bound N/2 in the Local Converse Theorem for GL(N) is sharp.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Algebra and Combinatorics
Faculty of Science > Research Groups > Number Theory (former - to 2017)
Depositing User: Pure Connector
Date Deposited: 02 Nov 2017 10:43
Last Modified: 24 May 2023 03:01
URI: https://ueaeprints.uea.ac.uk/id/eprint/65335
DOI: 10.1090/bproc/32

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