An algebraic theory for generalized Jordan chains and partial signatures in the Lagrangian Grassmannian

作者：Piccione Paolo^*; Tausk Daniel V

来源：Linear and Multilinear Algebra, 2010, 58(1): 89-103.

DOI：10.1080/03081080802383636

• symmetric bilinear forms
• generalized Jordan chains
• partial signatures
• Lagrangian Grassmannian
• Maslov index

We discuss an algebraic theory for generalized Jordan chains and partial signatures, that are invariants associated to sequences of symmetric bilinear forms on a vector space. We introduce an intrinsic notion of partial signatures in the Lagrangian Grassmannian of a symplectic space that does not use local coordinates, and we give a formula for the Maslov index of arbitrary real analytic paths in terms of partial signatures.

• 出版日期2010