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過去の記録 ～06/26｜次回の予定｜今後の予定 06/27～
| 開催情報 | 水曜日 17:00～18:00 数理科学研究科棟(駒場) 117号室 |
|---|---|
| 担当者 | 今井 直毅，ケリー シェーン |
次回の予定
2026年07月01日(水)
17:00-18:00 数理科学研究科棟(駒場) 117号室
石倉麟太郎 氏 (東京大学大学院数理科学研究科)
On boundedness of the number of cuspidal automorphic representations of Mp(4) ordinary at p
石倉麟太郎 氏 (東京大学大学院数理科学研究科)
On boundedness of the number of cuspidal automorphic representations of Mp(4) ordinary at p
[ 講演概要 ]
The notion of ordinary modular forms, introduced and developed in Hida theory, has played a central role in the study of p-adic families of automorphic forms. It is therefore natural to ask how this notion extends to automorphic representations of covering groups. This talk is concerned with p-ordinary cuspidal automorphic representations of the metaplectic group Mp(4) with holomorphic discrete series at infinity. Using two Iwahori-level Hecke operators, we define an ordinary projector and investigate the conditions for a representation to be ordinary at p. Fixing the level K, we prove a bound (depending only on K) for the number of genuine cuspidal automorphic representations of Mp(4) ordinary at p and containing nonzero K-fixed vectors, as the holomorphic weight varies.
The notion of ordinary modular forms, introduced and developed in Hida theory, has played a central role in the study of p-adic families of automorphic forms. It is therefore natural to ask how this notion extends to automorphic representations of covering groups. This talk is concerned with p-ordinary cuspidal automorphic representations of the metaplectic group Mp(4) with holomorphic discrete series at infinity. Using two Iwahori-level Hecke operators, we define an ordinary projector and investigate the conditions for a representation to be ordinary at p. Fixing the level K, we prove a bound (depending only on K) for the number of genuine cuspidal automorphic representations of Mp(4) ordinary at p and containing nonzero K-fixed vectors, as the holomorphic weight varies.
