Projects per year
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.
|Number of pages||12|
|Journal||Proceedings of the American Mathematical Society, Series B|
|Publication status||Published - 20 Feb 2018|
- 1 Finished