7 citations · 17 across the 12 of their papers we have counts for
12 papers
Monoidal Gröbner systems and categories of affine Brauer type
Sigiswald Barbier, Léo Schelstraete
We introduce an analogue of Gröbner bases, or equivalently, Bergman's diamond lemma, for linear (super)monoidal categories. It gives a systematic way to study monoidal ideals and t…
Diagram categories of Brauer type
Sigiswald Barbier
This paper introduces monoidal (super)categories resembling the Brauer category. For all categories, we can construct bases of the hom-spaces using Brauer diagrams. These categorie…
Operator Kantor Pairs
Sigiswald Barbier, Tom De Medts, Michiel Smet
Kantor pairs, (quadratic) Jordan pairs, and similar structures have been instrumental in the study of -graded Lie algebras and algebraic groups. We introduce the notion…
A general approach to constructing minimal representations of Lie supergroups
Sigiswald Barbier, Sam Claerebout
In this paper we describe an approach to generalise minimal representations to the super setting for Lie superalgebras obtained from Jordan superalgebras using the TKK construction…
A superunitary Fock model of the exceptional Lie supergroup
Sigiswald Barbier, Sam Claerebout
We construct a Fock model of the minimal representation of the exceptional Lie supergroup . Explicit expressions for the action are given by integrating to grou…
A Schrödinger model, Fock model and intertwining Segal-Bargmann transform for the exceptional Lie superalgebra
Sigiswald Barbier, Sam Claerebout
We construct two infinite-dimensional irreducible representations for : a Schrödinger model and a Fock model. Further, we also introduce an intertwining isomorphism. Thes…
A Fock Model and the Segal-Bargmann Transform for the Minimal Representation of the Orthosymplectic Lie Superalgebra
Sigiswald Barbier, Sam Claerebout, Hendrik De Bie
The minimal representation of a semisimple Lie group is a 'small' infinite-dimensional irreducible unitary representation. It is thought to correspond to the minimal nilpotent coad…
The blocks of the periplectic Brauer algebra in positive characteristic
Sigiswald Barbier, Anton Cox, Maud De Visscher
We determine the blocks of the periplectic Brauer algebra over any field of odd characteristic.
A minimal representation of the orthosymplectic Lie supergroup
Sigiswald Barbier, Jan Frahm
We construct a minimal representation of the orthosymplectic Lie supergroup , generalising the Schrödinger model of the minimal representation of to the super…
On structure and TKK algebras for Jordan superalgebras
Sigiswald Barbier, Kevin Coulembier
We compare a number of different definitions of structure algebras and TKK constructions for Jordan (super)algebras appearing in the literature. We demonstrate that, for unital sup…
The Joseph ideal for
Sigiswald Barbier, Kevin Coulembier
Using deformation theory, Braverman and Joseph obtained an alternative characterisation of the Joseph ideal for simple Lie algebras, which included even type A. In this note we ext…
Polynomial realisations of Lie (super)algebras and Bessel operators
Sigiswald Barbier, Kevin Coulembier
We study realisations of Lie (super)algebras in Weyl (super)algebras and connections with minimal representations. The main result is the construction of small realisations of Lie…