Let G = PGL(2, Qq). In this paper we shall investigate the group G of measurable currents taking values in G. The key observation is that G is acting by automorphisms on a homogeneous tree, which will play the role of the upper half plane in the case of PSL(2, R). Following the ideas of I.Μ. Gelfand, M.I. Graev and A.M. Vershik we shall construct an irreducible family of representations of G. The existence of such representations depends deeply on the non-vanishing of the first cohomology group H¹(G, π) for a suitable infinite dimensional π.
Kuhn, M. (2025). REPRESENTATIONS OF CURRENTS TAKING VALUES IN PGL(2, Qq). PURE AND APPLIED FUNCTIONAL ANALYSIS, 10(2), 362-381.
REPRESENTATIONS OF CURRENTS TAKING VALUES IN PGL(2, Qq)
Kuhn M. G.
2025
Abstract
Let G = PGL(2, Qq). In this paper we shall investigate the group G of measurable currents taking values in G. The key observation is that G is acting by automorphisms on a homogeneous tree, which will play the role of the upper half plane in the case of PSL(2, R). Following the ideas of I.Μ. Gelfand, M.I. Graev and A.M. Vershik we shall construct an irreducible family of representations of G. The existence of such representations depends deeply on the non-vanishing of the first cohomology group H¹(G, π) for a suitable infinite dimensional π.
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