6 research outputs found
Translation functors and decomposition numbers for the periplectic Lie superalgebra
We study the category of finite-dimensional integrable representations of the periplectic Lie superalgebra . We define an action of the Temperley-Lieb algebra with infinitely many generators and defining parameter on the category by translation functors. We also introduce combinatorial tools, called weight diagrams and arrow diagrams for resembling those for . 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 . We also prove that indecomposable projective modules in this category are multiplicity-free
Translation functors and decomposition numbers for the periplectic Lie superalgebra
We study the category of finite-dimensional integrable representations of the periplectic Lie superalgebra . We define an action of the Temperley-Lieb algebra with infinitely many generators and defining parameter on the category by translation functors. We also introduce combinatorial tools, called weight diagrams and arrow diagrams for resembling those for . 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 . We also prove that indecomposable projective modules in this category are multiplicity-free
Translation functors and decomposition numbers for the periplectic Lie superalgebra
We study the category of finite-dimensional integrable representations of the periplectic Lie superalgebra . We define an action of the Temperley-Lieb algebra with infinitely many generators and defining parameter on the category by translation functors. We also introduce combinatorial tools, called weight diagrams and arrow diagrams for resembling those for . 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 . We also prove that indecomposable projective modules in this category are multiplicity-free
The affine VW supercategory
We define the affine VW supercategory , which arises from studying the action of the periplectic Lie superalgebra on the tensor product of an arbitrary representation with several copies of the vector representation of . It plays a role analogous to that of the degenerate affine Hecke algebras in the context of representations of the general linear group; the main obstacle was the lack of a quadratic Casimir element in . When is the trivial representation, the action factors through the Brauer supercategory . Our main result is an explicit basis theorem for the morphism spaces of and, as a consequence, of . The proof utilises the close connection with the representation theory of . As an application we explicitly describe the centre of all endomorphism algebras, and show that it behaves well under the passage to the associated graded and under deformation