Higher Eisenstein elements, higher Eichler formulas and rank of Hecke algebras

Generalized Double Affine Hecke Algebras of Higher Rank

Meromorphic continuation of higher-rank Eisenstein series

Expanded version of a talk given in Tel Aviv, Israel, 22 March 2001. To trivialize the proof of meromorphic continuation of Eisenstein series, we want to use only standard facts, together with Bernstein’s formulation of a continuation principle. In particular, one should prove meromorphic continuation as a vector-valued function, from which one infers that the continuation is of moderate growth...

Higher Rank Graph Algebras

These are lecture notes of a course given by Alex Kumjian at the RMMC Summer School at the University of Wyoming, Laramie, June 1-5, 2015. Warning: little proofreading has been done.

Higher Rank Graph C∗-algebras

Building on recent work of Robertson and Steger, we associate a C∗–algebra to a combinatorial object which may be thought of as a higher rank graph. This C∗–algebra is shown to be isomorphic to that of the associated path groupoid. Various results in this paper give sufficient conditions on the higher rank graph for the associated C∗–algebra to be: simple, purely infinite and AF. Results concer...

Higher rank Einstein solvmanifolds

In this paper we study the structure of standard Einstein solvmanifolds of arbitrary rank. Also the validity of a variational method for finding standard Einstein solvmanifolds is proved.