Abstract
We formulate Nazarov–Wenzl type algebras Pˆd − for the representation theory of the periplectic Lie superalgebras p(n). We establish an Arakawa–Suzuki type functor to provide a connection between p(n)-representations and Pˆd −-representations. We also consider various tensor product representations for Pˆd −. The periplectic Brauer algebra Ad developed by Moon is a quotient of Pˆd −. In particular, actions induced by Jucys–Murphy elements can also be recovered under the tensor product representation of Pˆd −. Moreover, a Poincare–Birkhoff–Witt type basis for Pˆd − is obtained. A diagram realization of Pˆd − is also obtained.
Original language | English |
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Pages (from-to) | 345-372 |
Number of pages | 28 |
Journal | Journal of Algebra |
Volume | 501 |
DOIs | |
Publication status | Published - 2018 May 1 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory