Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II

Cyclic Representations of the Quantum Matrix Algebras

In this paper we give a complete classiication of the minimal cyclic M q (n)-modules and construct them explicitly. Also, we give a complete classiica-tion of the minimal cyclic modules of the so-called Dipper-Donkin quantum matrix algebra as well as of two other natural quantized matrix algebras. In the last part of the paper we relate the results to the De Concini { Procesi conjecture. 1. int...

Projective Representations of Reflection Groups Ii

SPECTRUM OF THE FOURIER-STIELTJES ALGEBRA OF A SEMIGROUP

For a unital foundation topological *-semigroup S whose representations separate points of S, we show that the spectrum of the Fourier-Stieltjes algebra B(S) is a compact semitopological semigroup. We also calculate B(S) for several examples of S.

The sl2 loop algebra symmetry of the twisted transfer matrix of the six vertex model at roots of unity

We discuss a family of operators which commute or anti-commute with the twisted transfer matrix of the six-vertex model at q being roots of unity: q = 1. The operators commute with the Hamiltonian of the XXZ spin chain under the twisted boundary conditions, and they are valid also for the inhomogeneous case. For the case of the anti-periodic boundary conditions, we show explicitly that the oper...

Representations of the Renormalization Group as Matrix Lie Algebra

Renormalization is cast in the form of a Lie algebra of matrices. By exponentiation, these matrices generate counterterms for Feynman diagrams with subdivergences. The matrices are triangular, and in general infinite. As representations of an insertion operator, the matrices provide explicit representations of the Connes-Kreimer Lie algebra. In fact, the right-symmetric nonassociative algebra o...