Simplified formalism of the algebra of partially transposed permutation operators with applications

Understand

Hereunder we continue the study of the representation theory of the algebra of permutation operators acting on the $n$-fold tensor product space, partially transposed on the last subsystem.

• We develop the concept of partially reduced irreducible representations, which allows to simplify significantly previously proved theorems and what is the most important derive new results for irreducible representations of the mentioned algebra.
• In our analysis we are able to reduce complexity of the central expressions by getting rid of sums over all permutations from symmetric group obtaining equations which are much more handy in practical applications.
• We also find relatively simple matrix representations for the generators of underlying algebra.