Mathematics Graduate Students Organization

Seminar:

Date: October 21

Fock spaces have been studied extensively over the last century, through quantum mechanics, combinatorics, operator algebras, etc. I will discuss operators represented on Fock spaces whose behavior on one tensor level depends only on two of its neighbors. Shaped by this behavior, the distributions represented through such operators have nice interpretations through special types of non-crossing partitions and lattice paths. We extend a number of results from prior works to our more general framework. These include the quadratic relation satisfied by the free cumulant generating function (or rather, a variant of it), the resolvent form of the generating function for the Wick polynomials, and classification results for the case when the vacuum state on the operator algebra is tracial. We also handle the generating functions in infinitely many variables by considering their matrix-valued versions. This is joint work done with Michael Anshelevich.