Density conditions with stabilizers for lattice orbits of Bergman kernels on bounded symmetric domains
Density conditions with stabilizers for lattice orbits of Bergman kernels on bounded symmetric domains
Abstract Let $$\pi _{\alpha }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>π</mml:mi><mml:mi>α</mml:mi></mml:msub></mml:math> be a holomorphic discrete series representation of a connected semi-simple Lie group G with finite center, acting on a weighted Bergman space $$A^2_{\alpha } (\Omega )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msubsup><mml:mi>A</mml:mi><mml:mi>α</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mi>Ω</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> on a bounded symmetric domain $$\Omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Ω</mml:mi></mml:math> , of formal dimension $$d_{\pi _{\alpha …