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Isospectral deformations of the Lagrangian Grassmannians

Jacques GasquiHubert Goldschmidt — 2007

Annales de l’institut Fourier

We study the special Lagrangian Grassmannian S U ( n ) / S O ( n ) , with n 3 , and its reduced space, the reduced Lagrangian Grassmannian X . The latter is an irreducible symmetric space of rank n - 1 and is the quotient of the Grassmannian S U ( n ) / S O ( n ) under the action of a cyclic group of isometries of order n . The main result of this paper asserts that the symmetric space X possesses non-trivial infinitesimal isospectral deformations. Thus we obtain the first example of an irreducible symmetric space of arbitrary rank 2 , which is...

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