We study Markov measures and p-adic random walks with the use of states on the Cuntz algebras Op. Via the Gelfand–Naimark–Segal construction, these come from families of representations of Op. We prove that these representations reflect selfsimilarity especially well. In this paper, we consider a Cuntz–Krieger type algebra where the adjacency matrix depends on a parameter q ( q=1 is the case of Cuntz–Krieger algebra). This is an ongoing work generalizing a construction of certain measures associated to random walks on graphs.

This corrigendum supplies different proofs for those places in the original paper where a certain theorem by Rickard was used.

The purpose of this article is to determine the representation type for all of the Hecke algebras of classical type. To do this, we combine methods from our previous work, which is used to obtain information on their Gabriel quivers, and recent advances in the theory of finite-dimensional algebras. The principal computation is for Hecke algebras of type B with two parameters. Then, we show that the representation type of Hecke algebras is governed by their Poincaré polynomials.

From Koornwinder's interpretation of big q-Legendre polynomials as spherical elements on the quantum SU(2) group an addition formula is derived for the big g-Legendre polynomial. The formula involves Al-Salam-Carlitz polynomials, little q-Jacobi polynomials and dual q-Krawtchouk polynomials. For the little q-ultraspherical polynomials a product formula in terms of a big q-Legendre polynomial follows by q-integration. The addition and product formula for the Legendre polynomials are obtained when q tends to 1.