Commutation matrices and commutation tensors

Commutation Relationships and Curvature Spin-tensors for Extended Spinor Connections

Extended spinor connections associated with composite spin-tensorial bundles are considered. Commutation relationships for covariant and multivariate differentiations and corresponding curvature spin-tensors are derived.

Commutation Structures

For fixed object X in a monoidal category, an X-commutation structure on an object A is just a map X⊗A → A⊗X. We study aspects of such structures in case A has a dual object. We consider a monoidal category V,⊗, I; for simplicity we let it be strict (the application we have in mind is anyway a category of endofuncors on a category, with composition as ⊗). Let X be an object in V, fixed througho...

Partial Commutation and Traces

Commutation with codes

The centralizer of a set of words X is the largest set of words C(X) commuting with X: XC(X) = C(X)X. It has been a long standing open question due to Conway, 1971, whether the centralizer of any rational set is rational. While the answer turned out to be negative in general, see Kunc 2004, we prove here that the situation is different for codes: the centralizer of any rational code is rational...

Commutation Relations and Markov Chains

It is shown that the combinatorics of commutation relations is well suited for analyzing the convergence rate of certain Markov chains. Examples studied include random walk on irreducible representations, a local random walk on partitions whose stationary distribution is the Ewens distribution, and some birth-death chains.