Translation functors and decomposition numbers for the periplectic Lie superalgebra \mathfrakp(n)

2016/10/26 by Balagovic, Martina, Daugherty, Zajj, Entova-Aizenbud, Inna +7
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1610.08470

Abstract

We study the category F_n of finite-dimensional integrable representations of the periplectic Lie superalgebra \mathfrakp(n). We define an action of the Temperley--Lieb algebra with infinitely many generators and defining parameter 0 on the category F_n by translation functors. We also introduce combinatorial tools, called weight diagrams and arrow diagrams for \mathfrakp(n) resembling those for \mathfrakgl(m|n). Using the Temperley--Lieb algebra action and the combinatorics of weight and arrow diagrams, we then calculate the multiplicities of standard and costandard modules in indecomposable projective modules and classify the blocks of F_n. We also prove that indecomposable projective modules in this category are multiplicity-free.

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