AN EIGENSPACE OF LARGE DIMENSION FOR A HECKE ALGEBRA ON AN (A)over tilde(2) BUILDING

作者：Mantero A M; Zappa A^*

来源：Journal of the Australian Mathematical Society, 2011, 91(1): 29-54.

DOI：10.1017/S1446788711001406

• buildings
• Hecke algebras
• Laplace operators
• Poisson kernel

Let Delta be an affine building of type (A)over tilde(2) 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 Delta. We prove that there exists a joint eigenspace of these operators having dimension greater than vertical bar W-0 vertical bar. This implies that there exist joint eigenfunctions of the Laplacians that cannot be expressed, via the Poisson transform, in terms of a finitely additive measure on the maximal boundary Omega of Delta.

• 出版日期2011-8