On calibrated representations of the degenerate affine Periplectic Brauer algebra

Abstract

We initiate the representation theory of the degenerate affine periplectic Brauer algebra on n strands by constructing its finite-dimensional calibrated representations when n=2. We show that any such representation that is indecomposable and does not factor through a representation of the degenerate affine Hecke algebra occurs as an extension of two semisimple representations with one-dimensional composition factors; and furthermore, we classify such repre-sentations with regular eigenvalues up to isomorphism.

Keywords

• periplectic brauer algebra
• degenerate affine periplectic brauer algebra
• degenerate affine hecke algebra
• calibrated representations; rhizomatic matrices