Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 16 (2021), 207 -- 222

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This work is licensed under a Creative Commons Attribution 4.0 International License.

ON CALIBRATED REPRESENTATIONS OF THE DEGENERATE AFFINE PERIPLECTIC BRAUER ALGEBRA

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

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.

2020 Mathematics Subject Classification: 17B10; 16G99.
Keywords: Periplectic Brauer algebra; degenerate affine Periplectic Brauer algebra; degenerate affine Hecke algebra; calibrated representations; rhizomatic matrices.

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Zajj Daugherty
Department of Mathematics,
City College of New York,
New York, NY 10031, USA.
e-mail: zdaugherty@gmail.com
https://zdaugherty.ccnysites.cuny.edu/


Iva Halacheva
Department of Mathematics,
Northeastern University,
Boston, MA 02115, USA.
e-mail: ihalacheva@gmail.com
https://sites.google.com/site/ivahalacheva3/


Mee Seong Im
Department of Mathematics,
United States Naval Academy,
Annapolis, MD 21402, USA.
e-mail: meeseongim@gmail.com
https://sites.google.com/site/meeseongim/


Emily Norton
Department of Mathematics,
TU Kaiserslautern, Germany.
e-mail: enorton@mpim-bonn.mpg.de
https://sites.google.com/view/emilynortonmath

http://www.utgjiu.ro/math/sma