How operators read factorial languages

Factorial languages arise in the context of Automata Theory. Essentially, they give the sequences of allowable operations an automaton can perform. The interplay with Operator Theory goes back to the work of Cuntz-Krieger and Matsumoto. A factorial language can be quantized in Hilbertian operators by using a Fock space construction, similar to what is done in Quantum Mechanics. In this talk I will present two algebras of operators that can be considered, and the level of rigidity they offer. Our study is carried in the intersection of C*-correspondences, subproduct systems, dynamical systems and subshifts. I will give the basic steps of our results with some comments on their proofs. The talk is based on joint works with Shalit and Barrett.

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