18 citations · 38 across the 11 of their papers we have counts for
11 papers
Difference Hierarchies for -Functions
Darlayne Addabbo, Maarten Bergvelt
We introduce hierarchies of difference equations (referred to as -systems) associated to the action of a (centrally extended, completed) infinite matrix group $GL_{\infty}^{(n)…
-Functions, Birkhoff Factorizations and Difference Equations
Darlayne Addabbo, Maarten Bergvelt
-systems and -systems are systems of integrable difference equations that have recently attracted much attention, and have wide applications in representation theory and stat…
Generalizations of -systems and Orthogonal Polynomials from Representation Theory
Darlayne Addabbo, Maarten Bergvelt
We briefly describe what tau-functions in integrable systems are. We then define a collection of tau-functions given as matrix elements for the action of on two-co…
Quadratic differential operators, Bicharacters and Products
Iana I. Anguelova, Maarten J. Bergvelt
For a commutative cocommutative Hopf algebra we study the relationship between a certain linear map defined via a bicharacter, an exponential of a quadratic differential operator a…
-Quantum Vertex Algebras
Maarten Bergvelt
We discuss a class of quantum vertex algebras where not only the commutativity of the vertex algebra is broken by a braiding map , but also the translation covariance is b…
Spin Calogero Particles and Bispectral Solutions of the Matrix KP Hierarchy
Maarten Bergvelt, Michael Gekhtman, Alex Kasman
Pairs of matrices whose commutator differ from the identity by a matrix of rank are used to construct bispectral differential operators with matrix coef…