On calibrated representations of the degenerate affine periplectic Brauer 
algebra

Daugherty, Zajj; Halacheva, Iva; Im, Mee Seong; Norton, Emily

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On calibrated representations of the degenerate affine periplectic Brauer algebra

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Norton, Emily
Max Planck Institute for Mathematics, Max Planck Society;

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https://www.utgjiu.ro/math/sma/v16/a16_11.html
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https://doi.org/10.48550/arXiv.1905.05148
(Preprint)

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Daugherty-Halacheva-Im-Norton_On calibrated representations of the degenerate affine Periplectic Brauer algebra_2021.pdf
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Citation

Daugherty, Z., Halacheva, I., Im, M. S., & Norton, E. (2021). On calibrated representations of the degenerate affine periplectic Brauer algebra. Surveys in Mathematics and its Applications, 16, 207-222.

Cite as: https://hdl.handle.net/21.11116/0000-000A-1C20-3

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.