# On the first occurrence of cuspidal representations of symplectic groups Academic Article

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### abstract

• 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.

### publication date

• January 1, 2006