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A DESCRIPTION OF ALL IRREDUCIBLE REPRESENTATIONS OF K PGL20
THE IRREDUCIBLE UNITARY REPRESENTATIONS OF PGL2fi AND THEIR CHARACTERS
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AflK algebraically irreducible representation Assume Chapter compact support compute conductor conjugacy classes Corollary correspond decomposes simply decomposition denote direct sum double cosets equation equivalent explicit finite finite-dimensional follows Fourier transform functions on G g e G Haar measure Hilbert space homomorphism implies induced representation inequivalent integral inversion formula irreducible repre irreducible unitary representation isomorphism K-module lemma mapping matrix coefficients Mautner multiplicative character non-regular elements norm occurs in res operator ord(b ord(c orthogonal orthonormal base Plancherel's formula primitive mod primitive mod pm principal series Proof quadratic extension ramified real-valued reducible mod representations of G res T contains res T decomposes restrictions Schur orthogonality relations Seiten sentation series of G space H spherical functions subspace TflK Theorem 3.3 trace unique unramified discrete series vector space write