A canonical map between Hecke algebras

Mori, Andrea ; Terracini, Lea

Bollettino della Unione matematica italiana, Série 8, 2B (1999) no. 2, pp. 429-452.

Résumé

Sia $D$ un corpo di quaternioni indefinito su $\mathbf{Q}$ di discriminante $\Delta$ e sia $\Gamma$ il gruppo moltiplicativo degli elementi di norma 1 in un ordine di Eichler di $D$ di livello primo con $\Delta$. Consideriamo lo spazio $S_{k}(\Gamma)$ delle forme cuspidali di peso $k$ rispetto a $\Gamma$ e la corrispondente algebra di Hecke $\mathbf{H}^{D}$. Utilizzando una versione della corrispondenza di Jacquet-Langlands tra rappresentazioni automorfe di $D^{\times}$ e di $GL_{2}$, realizziamo $\mathbf{H}^{D}$ come quoziente dell'algebra di Hecke classica di livello $N\Delta$. Questo risultato permette di ottenere informazioni sulla struttura dell'algebra $\mathbf{H}^{D}$ e di definire una struttura intera per lo spazio $S_k(\Gamma)$.

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