Ask a Question

Prefer a chat interface with context about you and your work?

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>๐”ค</mml:mi><mml:mo>,</mml:mo><mml:mi>K</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>-cohomology

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>๐”ค</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 (๐”ค,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 โ€ฆ