Relative singular value decomposition and applications to LS-category.

Let Sp (n) be the symplectic group of quaternionic (n × n) -matrices. For any 1 ≤ k ≤ n , an element A of Sp (n) can be decomposed in A = [ α T β P ] with P a (k × k) -matrix. In this work, starting from a singular value decomposition of P , we obtain what we call a relative singular value decomposition of A. This feature is well adapted for the study of the quaternionic Stiefel manifold X n , k , and we apply it to the determination of the Lusternik-Schnirelmann category of Sp (k) in X 2 k − j , k , for j = 0 , 1 , 2. [ABSTRACT FROM AUTHOR]