ON A MULTIPLICITY FORMULA OF WEIGHTS OF REPRESENTATIONS OF SO-ASTERISK(2N) AND RECIPROCITY THEOREMS FOR SYMPLECTIC GROUPS

Authors
LEUNG EY TONTHAT T
Citation
Ey. Leung et T. Tonthat, ON A MULTIPLICITY FORMULA OF WEIGHTS OF REPRESENTATIONS OF SO-ASTERISK(2N) AND RECIPROCITY THEOREMS FOR SYMPLECTIC GROUPS, Proceedings of the American Mathematical Society, 123(4), 1995, pp. 1281-1288
Citations number
17
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Proceedings of the American Mathematical Society → ACNP
ISSN journal
00029939
Volume
123
Issue
4
Year of publication
1995
Pages
1281 - 1288
Database
ISI
SICI code
0002-9939(1995)123:4<1281:OAMFOW>2.0.ZU;2-M
Abstract
A formula relating the multiplicity of a weight of a holomorphic discr ete series of the group SO(2n) to the frequency of occurrence of an i rreducible holomorphically induced representation of the group Sp(2n, C) in an n-fold tenser product of irreducible symmetric representation s of Sp(2n, C) is given. Reciprocity theorems relating holomorphic dis crete series of SO(2n) (resp. Sp(2n, R)) to holomorphically induced r epresentations of Sp(2k,C) (resp. SO(N, C)) are also derived.