منابع مشابه
THE NONARCHIMEDEAN THETA CORRESPONDENCE FOR GSp(2) AND GO(4)
In this paper we consider the theta correspondence between the sets Irr(GSp(2, k)) and Irr(GO(X)) when k is a nonarchimedean local field and dimk X = 4. Our main theorem determines all the elements of Irr(GO(X)) that occur in the correspondence. The answer involves distinguished representations. As a corollary, we characterize all the elements of Irr(O(X)) that occur in the theta correspondence...
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We consider both local and global theta correspondences for GSp4 and GSO4,2. Because of the accidental isomorphism PGSO4,2 PGU2,2, these correspondences give rise to those between GSp4 and GU2,2 for representations with trivial central characters. In the global case, using this relation, we characterize representations with trivial central character, which have Shalika period on GU(2, 2) by the...
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Consider real reductive group G, as defined in [Wal88]. Let Π be an irreducible admissible representation of G with the distribution character ΘΠ, [Har51]. Denote by uΠ the lowest term in the asymptotic expansion of ΘΠ, [BV80]. This is a finite linear combination of Fourier transforms of nilpotent coadjoint orbits, uΠ = ∑ O cOμ̂O. As shown by Rossmann, [Ros95], the closure of the union of the ni...
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ژورنال
عنوان ژورنال: Journal of the Royal Asiatic Society of Great Britain & Ireland
سال: 1894
ISSN: 0035-869X,2051-2066
DOI: 10.1017/s0035869x00144004