Pure Maths Colloquium: Primitive Representations of U(1, 1)(O)
19 September 2016 16:00 in CM221
Let O be the ring of integers of a ramified quadratic extension E/F of local non-archimedian field. The group U(1, 1)(O) the group of matrices g ∈ GL(2, O) that preserves the form h : E^2 × E^2 → E given by
h((x, y),(z, w)) = (x^∗)w − (y^∗)z.
We construct a family of irreducible representations ρ , called primitive, of U(1, 1)(O) such that any irreducible representation σ of U(1, 1)(O) is of the form ρ ⊗ χ ◦ det, for some linear character χ of O^×.
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