In Claus Sorenson's PhD thesis, he proves a theorem about level lifting of paramodular forms whose associated automorphic representation has component $\pi_{\infty}$ that is the "cohomological holomorphic discrete series representation". But it isn't clear to me why the definite article is appropriate, or how to translate this description into Blattner parameters. So what is this representation, and why it is unique as defined above?
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1$\begingroup$ It's the unique holomorphic discrete series automorphic representation of $PGSp(4)$ which is cohomological with trivial coefficients. This is the one associated to a genus 2 Siegel modular form of parallel weight 3. $\endgroup$– David LoefflerJun 5, 2015 at 6:16
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