Representation theory and the branching graph for the family of Turaev algebras

We consider the family of algebras $\{H_q^{1,n}\}_{n=1}^\infty$, where $H_q^{1,n}$ is obtained by changing the first generator in the group algebra of the symmetric group $S_{n+1}$. We describe the irreducible representations of these algebras and construct the branching graph of the family $\{H_q^{1,n}\}_{n=1}^\infty$. Bibliography: 6 titles.