Affine Periplectic Brauer Algebras

2016/10/25 by Chen, Chih-Whi, Peng, Yung-Ning
#17B10 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1610.07781

Abstract

We formulate Nazarov-Wenzl type algebras \widehatP_d^- for the representation theory of the Periplectic Lie superalgebras \mathfrakp(n). We establish a Arakawa-Suzuki type theorem to provide a connection between \mathfrakp(n)-representations and \widehatP_d^--representations. We also consider various tensor product representations for \widehatP_d^-. The periplectic Brauer algebra A_d defined by Moon is an quotient of \widehatP_d^-. In particular, actions induced by Jucys-Murphy elements can be obtained under the tensor product representation of \widehatP_d^-. Also, a Poincare-Birkhoff-Witt type basis for \widehatP_d^- is obtained.

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