Algebra- och geometriseminarium: Affine periplectic Brauer algebras
- Plats: Ångströmlaboratoriet 64119
- Föreläsare: Chih-Whi Chen (Uppsala)
- Kontaktperson: Volodymyr Mazorchuk
The periplectic Lie superalgebra p(n) is a superanalogue
of the orthogonal or symplectic Lie algebra preserving an odd
non-degenerate symmetric or skew symmetric bilinear form. However,
the representation theory of the periplectic Lie superalgebra is still not
well-understood. One of the main reasons is that many classical methods
in representation theory are not applicable. In particular, the center of
its universal enveloping algebra fails to provide us with information about
the blocks in the respective categories.
Approximately 15 years ago Moon used generator and relation to define the
periplectic Brauer algebra, which describes the endomorphism algebra of
tensor power of natural representations of p(n). Recently, Kujawa and Tharp
gave diagrammatic description of this algebra. It has also recently been studied
by Coulembier, Coulembier-Ehrig and Benkart et al.
Arakawa-Suzuki functor provide the connection between gl(n)-modules and
modules over (degenerate) affine Hecke algebra. The type BCD analogue is
the (degenerated) affine Nazarov-Wenzl algebra. In this talk, we introduce
the representation theory of p(n). We will formulate an affine version of
periplectic Brauer algebra and obtain the Poincare-Birkhoff-Witt type basis.
This is joint work with Yung-Ning Peng.