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EnglishLet Δ be an affine building of type Ã2 and let A be its fundamental apartment. We consider the set U_0 of vertices of type 0 of A and prove that the Hecke algebra of all W_0-invariant difference operators with constant coefficients acting on U_0 has three generators. This property leads us to define three Laplace operators on vertices of type 0 of Δ. We prove that there exists a joint eigenspace of these operators having dimension greater than |W_0|. This implies that there exist joint eigenfunctions of the Laplacians that cannot be expressed, via the Poisson transform, in terms of a finitely addittive measure on the maximal boundary Ω of Δ.
AN EIGENSPACE OF LARGE DIMENSION FOR A HECKE ALGEBRA ON AN A_2 BUILDING / Anna Maria Mantero; Anna Zappa. - In: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY. - ISSN 1446-7887. - STAMPA. - 91 n.1(2011), pp. 29-54.
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| Titolo: | AN EIGENSPACE OF LARGE DIMENSION FOR A HECKE ALGEBRA ON AN A_2 BUILDING |
| Autori: | |
| Data di pubblicazione: | 2011 |
| Rivista: | |
| Citazione: | AN EIGENSPACE OF LARGE DIMENSION FOR A HECKE ALGEBRA ON AN A_2 BUILDING / Anna Maria Mantero; Anna Zappa. - In: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY. - ISSN 1446-7887. - STAMPA. - 91 n.1(2011), pp. 29-54. |
| Abstract: | Let Δ be an affine building of type Ã2 and let A be its fundamental apartment. We consider the set U_0 of vertices of type 0 of A and prove that the Hecke algebra of all W_0-invariant difference operators with constant coefficients acting on U_0 has three generators. This property leads us to define three Laplace operators on vertices of type 0 of Δ. We prove that there exists a joint eigenspace of these operators having dimension greater than |W_0|. This implies that there exist joint eigenfunctions of the Laplacians that cannot be expressed, via the Poisson transform, in terms of a finitely addittive measure on the maximal boundary Ω of Δ. |
| Handle: | http://hdl.handle.net/11567/296722 |
| Appare nelle tipologie: | 01.01 - Articolo su rivista |
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