Maslov indices on the metaplectic group M p ( n )

Maurice De Gosson

Annales de l'institut Fourier (1990)

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

Abstract

top
We use the properties of M p ( n ) to construct functions μ ℓ : M p ( n ) → Z 8 associated with the elements ℓ of the lagrangian grassmannian Λ (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 M p ( n ) and a subset of S p ( n ) × Z 8 , equipped with appropriate algebraic and topological structures.

How to cite

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.