New reflection matrices for theU_q(gl(m|n)) case

Abstract

We examine super symmetric representations of the B-type Hecke algebra. We exploit such representations to obtain new non-diagonal solutions of the reflection equation associated to the super algebra U q (gl(m|n)). The boundary super algebra is briefly discussed and it is shown to be central to the super symmetric realization of the B-type Hecke algebra

Fermionic reflection matrices

“…As before, the nonzero entries of the reflection matrix lie solely along the principal and the secondary diagonals of the bosonic submatrices, or along the principal and one minor antidiagonal below or above the secondary one. For the symmetric Dynkin diagram, such nondiagonal solutions were first obtained in [13], albeit from a different point of view, where the nondiagonal entries lie only along the secondary diagonal.…”

On boundary superalgebras

“…A new class of non-diagonal reflection matrices associated to U q (glm|n) was recently derived in [31]. Specifically, first Then the non diagonal matrices read as:…”

On the \mathcal {U}_{q}[sl(2)] Temperley–Lieb reflection matrices

“…Although being a hard problem, the direct computation has been used to derive the solutions of the boundary Yang-Baxter equation (1.2) for given R. For instance, we mention the solutions with R matrix based in non-exceptional Lie algebras [19,20] and superalgebras [21,22]. The regular K-matrices for the exceptional U q [G 2 ] vertex model were obtained in [23].…”