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Characters of Speh representations and Lewis Carroll identity. (Characters of Speh representations and Lewis Caroll identity.) (English) Zbl 1163.22008
Speh representations are the building blocks for the unitary dual of \(GL(n,A)\), where \(A\) is a central division algebra over a non-Archimedean local field. The characters of irreducible unitary representations can be computed from the characters of Speh representations, and a formula is known by Tadić. The authors give a new and elementary proof of the Tadić formula for the characters of the Speh representation of \(GL(n,A)\). Their proof follows from a combinatorial identity, which is already known under the name of Lewis Caroll identity.

MSC:
22E50 Representations of Lie and linear algebraic groups over local fields
11F70 Representation-theoretic methods; automorphic representations over local and global fields
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