Maximal degenerate representations of SL(n+1,H)

Abstract: The infinitesimal method is applied to study some maximal degenerate representations of $ SL(n+1,\Bbb{H})$. The irreducibility and unitarizability of these representations are determined and the composition series is given in the reducible case. The existence of intertwining operators is established for the differentiated Lie algebra representations. On the group level, the intertwining operators are given by an explicit integral formula.

Keywords: maximal degenerate representations, quaternionic Lie group, special linear group, infinitesimal method, irreducibility, unitarizability, composition series, intertwining operators, integral formulas

Classification (MSC91): 20G20; 20G05, 22E45

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