The **automorphic type** of a Siegel newform $f \in S_{k,j}(\Gamma)$ of degree 2 is a letter indicating the type of the Arthur parameters of the automorphic representation $\pi$ associated to $f$.
These fall into six classes of (packets of ) representations:

(F) - finite-dimensional (in fact, one-dimensional) representations. These correspond to Siegel-Eisenstein series.

(Q), (P), (B) - representations induced from cuspidal representations of the three proper parabolic subgroups (Klingen, Siegel and Borel respectively). For example, Klingen-Eisenstein series are of type (Q) and Saito-Kurokawa lifts are of type (P).

(Y) - Yoshida type, the irreducible quotient of the tensor product of two distinct cuspidal automorphic representations of ${\rm GL}_2$, corresponding to Yoshida lifts.

(G) - General type, which contains the remaining representations. These are characterized by admitting a functorial transfer to a cuspidal automorphic representation of ${\rm GL}_4$

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**Knowl status:**

- Review status: beta
- Last edited by Eran Assaf on 2023-07-13 01:02:00

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- 2023-07-13 01:02:00 by Eran Assaf
- 2022-08-31 11:02:17 by Eran Assaf
- 2022-08-31 11:00:52 by Eran Assaf
- 2022-08-31 10:59:43 by Eran Assaf
- 2022-08-31 10:59:26 by Eran Assaf
- 2022-08-31 10:58:23 by Eran Assaf
- 2022-08-31 10:49:41 by Eran Assaf
- 2022-08-31 10:46:21 by Eran Assaf
- 2022-08-31 10:43:23 by Eran Assaf

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