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Affine periplectic Brauer algebras
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry. Natl Ctr Theoret Sci, Math Div, Taipei 10617, Taiwan.
Natl Cent Univ, Dept Math, Chungli 32054, Taiwan..
2018 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 501, p. 345-372Article in journal (Refereed) Published
Abstract [en]

We formulate Nazarov-Wenzl type algebras (P) over cap (-)(d) 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 (P) over cap (-)(d)-representations. We also consider various tensor product representations for (P) over cap (-)(d). The periplectic Brauer algebra A(d) developed by Moon is a quotient of (P) over cap (-)(d). In particular, actions induced by Jucys-Murphy elements can also be recovered under the tensor product representation of (P) over cap (-)(d). Moreover, a Poincare-Birkhoff-Witt type basis for (P) over cap (-)(d) is obtained. A diagram realization of PI is also obtained.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE , 2018. Vol. 501, p. 345-372
Keywords [en]
Periplectic Lie superalgebras, Marked Brauer category, Periplectic Brauer algebra, Affine Nazarov-Wenzl algebra, Jucys-Murphy elements, Poincare-Birkhoff-Witt basis
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:uu:diva-350722DOI: 10.1016/j.jalgebra.2018.01.005ISI: 000427214100018OAI: oai:DiVA.org:uu-350722DiVA, id: diva2:1206172
Available from: 2018-05-16 Created: 2018-05-16 Last updated: 2018-05-16Bibliographically approved

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Chen, Chih-Whi

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