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Branching of unitary <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="normal">O</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-representations with non-trivial <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:mi>๐ค</mml:mi><mml:mo>,</mml:mo><mml:mi>K</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>-cohomology
Let G=O(1,n+1) with maximal compact subgroup K and let ฮ be a unitary irreducible representation of G with non-trivial (๐ค,K)-cohomology. Then ฮ occurs inside a principal series representation of G, induced from the O(n)-representation โ p (โ n ) and characters of a minimal parabolic subgroup of G at the โฆ