Journal of Combinatorial Algebra


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Volume 2, Issue 1, 2018, pp. 19–46
DOI: 10.4171/JCA/2-1-2

Published online: 2018-02-08

The periplectic Brauer algebra II: Decomposition multiplicities

Kevin Coulembier[1] and Michael Ehrig[2]

(1) University of Sydney, Australia
(2) University of Sydney, Australia

We determine the Jordan–Hölder decomposition multiplicities of projective and cell modules over periplectic Brauer algebras in characteristic zero. These are obtained by developing the combinatorics of certain skew Young diagrams.We also establish a useful relationship with the Kazhdan–Lusztig multiplicities of the periplectic Lie supergroup.

Keywords: Periplectic Lie superalgebra, periplectic Brauer algebra, decomposition multiplicities, (skew) Young diagrams, standardly based algebras

Coulembier Kevin, Ehrig Michael: The periplectic Brauer algebra II: Decomposition multiplicities. J. Comb. Algebra 2 (2018), 19-46. doi: 10.4171/JCA/2-1-2