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Symplectic Induction and Semisimple Orbits
Author(s) -
Chuah MengKiat
Publication year - 2005
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609305004364
Subject(s) - symplectic geometry , mathematics , moment map , symplectomorphism , pure mathematics , symplectic representation , symplectic manifold , symplectic matrix , symplectic group , orbit (dynamics) , lie group , algebra over a field , engineering , aerospace engineering
Symplectic induction was first introduced by Weinstein as the symplectic analogue of induced representations, and was further developed by Guillemin and Sternberg. This paper deals with the case where the symplectic manifold in question is a semisimple coadjoint orbit of a Lie group. In this case, the construction is generalized by adding a smooth mapping, in order to obtain various symplectic forms. In particular, when the orbit is elliptic, a study of the complex geometry shows that quantization commutes with induction. 2000 Mathematics Subject Classification 22F30, 53C55, 53D05.