Generic Linear Recurrent Sequences and Related Topics

The aim of the book is to introduce and develop the elementary theory of generic linear recurrent relations and to show how it provides a natural framework to put into a unified perspective many seemingly unrelated subjects. Among them: traces of an endomorphism and the Cayley-Hamilton theorem, Generic Linear ODEs and their Wronskians, the exponential of a matrix with indeterminate entries (revisiting Putzer’s method), universal decomposition algebras of a polynomial into the product of two monic polynomials of fixed smaller degree, vertex operators obtained via Schubert calculus tools (Giambelli’s formula). Emphasis will be put on the characterization of decomposable tensors of an exterior power of a free abelian group of possibly infinite rank. The classical example of the Hirota bilinear form of the Kadomtsev-Petshiasvilii (KP) hierarchy, seen as equations of the Plu ̈cker embedding of an infinite-dimensional Grassmannian, will be included. The research that lead to the present paper was partially supported by a grant of the group GNSAGA of INdAM