Maslov indices on the metaplectic group

Maurice De Gosson

Annales de l'institut Fourier (1990)

  • Volume: 40, Issue: 3, page 537-555
  • ISSN: 0373-0956

Abstract

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We use the properties of to construct functions associated with the elements of the lagrangian grassmannian (n) which generalize the Maslov index on Mp(n) defined by J. Leray in his “Lagrangian Analysis”. We deduce from these constructions the identity between and a subset of , equipped with appropriate algebraic and topological structures.

How to cite

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De Gosson, Maurice. "Maslov indices on the metaplectic group $Mp(n)$." Annales de l'institut Fourier 40.3 (1990): 537-555. <http://eudml.org/doc/74887>.

@article{DeGosson1990,
abstract = {We use the properties of $Mp(n)$ to construct functions $\mu _\{\ell \}: Mp(n)\rightarrow \{\bf Z\}_ 8$ associated with the elements $\ell $ of the lagrangian grassmannian $\Lambda $ (n) which generalize the Maslov index on Mp(n) defined by J. Leray in his “Lagrangian Analysis”. We deduce from these constructions the identity between $Mp(n)$ and a subset of $Sp(n)\times \{\bf Z\}_ 8$, equipped with appropriate algebraic and topological structures.},
author = {De Gosson, Maurice},
journal = {Annales de l'institut Fourier},
keywords = {metaplectic group; Fourier transform; signature; index of inertia; Lagrangian; Grassmannian; Maslov index},
language = {eng},
number = {3},
pages = {537-555},
publisher = {Association des Annales de l'Institut Fourier},
title = {Maslov indices on the metaplectic group $Mp(n)$},
url = {http://eudml.org/doc/74887},
volume = {40},
year = {1990},
}

TY - JOUR
AU - De Gosson, Maurice
TI - Maslov indices on the metaplectic group $Mp(n)$
JO - Annales de l'institut Fourier
PY - 1990
PB - Association des Annales de l'Institut Fourier
VL - 40
IS - 3
SP - 537
EP - 555
AB - We use the properties of $Mp(n)$ to construct functions $\mu _{\ell }: Mp(n)\rightarrow {\bf Z}_ 8$ associated with the elements $\ell $ of the lagrangian grassmannian $\Lambda $ (n) which generalize the Maslov index on Mp(n) defined by J. Leray in his “Lagrangian Analysis”. We deduce from these constructions the identity between $Mp(n)$ and a subset of $Sp(n)\times {\bf Z}_ 8$, equipped with appropriate algebraic and topological structures.
LA - eng
KW - metaplectic group; Fourier transform; signature; index of inertia; Lagrangian; Grassmannian; Maslov index
UR - http://eudml.org/doc/74887
ER -

References

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  1. [G1] M. de GOSSON, La définition de l'indice de Maslov sans hypothèse de transversalité, C.R. Acad. Sci. Paris, t. 310, Série I (1990), 279-282. Zbl0705.22012MR91e:58189
  2. [G2] M. de GOSSON, La relation entre Sp∞, revêtement universel du groupe symplectique Sp et Sp × ℤ, C.R. Acad. Sci. Paris, t. 310, Série I (1990), 245-248. Zbl0732.22001
  3. [G3] M. de GOSSON, The structure of q-symplectic geometry, to appear in : Journal des Mathématiques Pures et Appliquées, Paris, 1990. Zbl0829.58015
  4. [GS] V. GUILLEMIN, S. STERNBERG, Geometric Asymptotics, Math. Surveys 14, A.M.S., Providence, R.I., 1977. Zbl0364.53011MR58 #24404
  5. [L] J. LERAY, Lagrangian Analysis and Quantum Mechanics, The M.I.T. Press, Cambridge, London, 1981, (Analyse Lagrangienne, R.C.P. 25, Strasbourb, 1978 ; Collège de France 1976-1977). 
  6. [LV] G. LION, M. VERGNE, The Weil representation, Maslov index and Theta series, Birkhäuser (Progress in Mathematics), Boston, Basel, Bruxelles, 1980. Zbl0444.22005
  7. [W] A. WEIL, Sur certains groupes d'opérateurs unitaires, Acta Math., 111, 1964. Zbl0203.03305MR29 #2324

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