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wave front

Journal of the Institute of Mathematics of Jussieu (1)

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ON THE FIRST OCCURRENCE OF CUSPIDAL REPRESENTATIONS OF SYMPLECTIC GROUPS
David Ginzburg, Nadya Gurevich
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 5 / Issue 1 / January 2006

Published online by Cambridge University Press:

03 November 2005, pp. 35-52

Print publication:

January 2006
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We study the first occurrence of a cuspidal representation $\pi$ of $\mathrm{Sp}_{2n}(\mathbb{A})$ in the tower of split orthogonal groups under symplectic-orthogonal theta lift. We give upper and lower bounds for the first occurrence in terms of the wave front of $\pi$. Besides we describe a class of small cuspidal representations whose first occurrence is the maximal possible.