Theta Dichotomy and Doubling Epsilon Factors
نویسندگان
چکیده
In this work, we aim to prove the theta dichotomy conjecture for dual dual pairs of type ( ̃ Sp(W ),O(V )) with dim(V ) odd. The crux of the proof relies on the analysis the reducibility of a certain a degenerate principal series representation of the group ̃ Sp(W ′) having double the rank of ̃ Sp(W ). This analysis is carried out by way of a normalized standard intertwining operator which is also used to define an epsilon factor coming from the doubling integral construction of PiatetskiShapiro and Rallis. In this paper, we also illustrate the connection between the doubling epsilon factor and the theta dichotomy conjecture.
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