Symmetric association schemes attached to finite upper half planes over rings. (English) Zbl 1037.05051
Summary: The finite upper half planes over finite fields and rings are finite analogues of the Poincaré upper half plane. The general linear group \(G\) acts transitively on the finite upper half plane. Let \(K\) denote the stabilizer of a point. In the case of fields, it is well known that the pair \((G,K)\) is a Gelfand pair. In this paper, we show that \((G,K)\) is also a Gelfand pair in the case of rings.
MSC:
| 05E30 | Association schemes, strongly regular graphs |
| 05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
| 11T60 | Finite upper half-planes |
Keywords:
Finite upper half plane; Poincaré distance; General linear group; Association scheme; Gelfand pair; Finite ringReferences:
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