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Secondary Whittaker functions for \(P_J\)-principal series representations of \(\text{Sp}(3,\mathbb R)\). (English) Zbl 1109.22009

For \(\text{Sp}(3,\mathbb R)\) the authors construct explicit formulas for the power series solutions at the regular singularity of the holonomic system coming from the principal series representation induced from the second parabolic subgroup \(P_J\). These secondary Whittaker functions are confluent hypergeometric series in three variables which are not simple \(\Gamma\)-series.

MSC:

22E46 Semisimple Lie groups and their representations
11F70 Representation-theoretic methods; automorphic representations over local and global fields
33C80 Connections of hypergeometric functions with groups and algebras, and related topics
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