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- Title
COMPUTATION OF A TWISTED CHARACTER OF A SMALL REPRESENTATION OF GL(3, E).
- Authors
FLICKER, YUVAL Z.; ZINOVIEV, DMITRII
- Abstract
Let E/F be a quadratic extension of p-adic fields, p ≠ 2. Let $x \mapsto \overline{x}$ be the involution of E over F. The representation π of GL(3, E) normalizedly induced from the trivial representation of the maximal parabolic subgroup is invariant under the involution $\sigma(g) = J{}^t\overline{g}^{-1}J$. We compute - by purely local means - the σ-twisted character $\chi_\pi^\sigma$ of π. We show that it is σ-unstable, namely its value at one σ-regular-elliptic conjugacy class within a stable such class is equal to negative its value at the other such conjugacy class within the stable class, or zero when the σ-regular-elliptic stable conjugacy class consists of a single such conjugacy class. Further, we relate this twisted character to the twisted endoscopic lifting from the trivial representation of the "unstable" twisted endoscopic group U(2, E/F) of GL(3, E). In particular π is σ-elliptic, that is, $\chi_\pi^\sigma$ is not identically zero on the σ-elliptic set.
- Subjects
REPRESENTATIONS of algebras; P-adic fields; CONJUGACY classes; P-adic numbers; ALGEBRAIC fields; QUADRATIC fields; MATHEMATICAL analysis
- Publication
International Journal of Number Theory, 2012, Vol 8, Issue 5, p1153
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042112500704