B V Rajarama Bhat: Unitary orthonormal bases for finite dimensional inclusions

Speaker
B V Rajarama Bhat, Indian Statistical Institute,  Bangalore

Abstract
We study unitary orthonormal bases in the sense of Pimsner and Popa for inclusions of  finite dimensional von Neumann algebras with a prescribed conditional expectation map.   These generalize complex Hadamard matrices and Weyl unitaries. The existence of unitary orthonormal bases has several  applications in subfactor theory.

We derive some interesting necessary conditions for the existence of such bases. Whether these conditions are sufficient is an open question. For some special cases we provide explicit but intricate constructions of unitary orthonormal bases.  This talk is based on a joint work with Keshab Chandra Bakshi