On calibrated representations of the degenerate affine periplectic Brauer algebra

2019/05/13 by Daugherty, Zajj, Halacheva, Iva, Im, Mee Seong +1
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1905.05148

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 representations with regular eigenvalues up to isomorphism.

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