an:03851409
Zbl 0536.22018
G??rardin, P.
Harmonic functions on buildings of reductive split groups
EN
Operator algebras and group representations, Proc. int. Conf., Neptun/Rom. 1980, Vol. I. Monogr. Stud. Math. 17, 208-221 (1984).
1984
a
22E35 43A85 31B25
symmetric space; harmonic functions; G-invariant differential operators; mean value property; commutative function algebra; Satake compactification; minimal parabolic subgroups; p-adic case; reductive algebraic group; buildings; distinguished boundary
[For the entire collection see Zbl 0515.00017.]
Let G be a connected reductive split group of adjoint type over p-adic field. After constructing the building \(X=X(G)\) (following Bruhat-Tits), the author introduces a compactification of X analogous to the Satake compactification of a symmetric space, then he defines harmonic functions and shows, in certain cases, that they are defined by their boundary values on the distinguished boundary.
F.Rouvi??re
Zbl 0515.00017