Tau-functions, Grassmannians and rank one conditions

Harmonic Functions on Classical Rank One Balls

Integrable Systems and Rank-one Conditions for Rectangular Matrices

We give a determinantal formula for tau functions of the KP hierarchy in terms of rectangular constant matrices A, B, and C satisfying a rank-one condition. This result is shown to generalize and unify many previous results of different authors on constructions of tau functions for differential and difference integrable systems from square matrices satisfying rank-one conditions. In particular,...

Zeta Functions for Elements of Entropy Rank One Actions

An algebraic Z-action of entropy rank one is one for which each element has finite entropy. Using the structure theory of these actions due to Einsiedler and Lind, this paper investigates dynamical zeta functions for elements of the action. An explicit periodic point formula is obtained leading to a uniform parameterization of the zeta functions that arise in expansive components of an expansiv...

Finite rank vector bundles on inductive limits of grassmannians

If P is the projective ind-space, i.e. P is the inductive limit of linear embeddings of complex projective spaces, the Barth-Van de Ven-Tyurin (BVT) Theorem claims that every finite rank vector bundle on P is isomorphic to a direct sum of line bundles. We extend this theorem to general sequences of morphisms between projective spaces by proving that, if there are infinitely many morphisms of de...

Rank and dimension functions

In this paper, we invoke the theory of generalized inverses and the minus partial order on the study of regular matrices over a commutative ring to define rank–function for regular matrices and dimension–function for finitely generated projective modules which are direct summands of a free module. Some properties held by the rank of a matrix and the dimension of a vector space over a field are ...