11 papers
Representations of the Lie superalgebra of superderivations of the Grassmann algebra at infinity
Lucas Calixto, Crystal Hoyt
The Lie superalgebra is defined to be the direct limit of the simple finite-dimensional Cartan type Lie superalgebras as goes to infinity, where denot…
Representations of affine Lie superalgebras and their quantization in type A
Luan Pereira Bezerra, Lucas Calixto, Vyacheslav Futorny +1
We construct a new family of irreducible modules over any basic classical affine Kac-Moody Lie superalgebra which are induced from modules over the Heisenberg subalgebra. We also o…
Finite-dimensional representations of map superalgebras
Lucas Calixto, Tiago Macedo
We obtain a complete classification of all finite-dimensional irreducible modules over classical map superalgebras, provide formulas for their (super)characters and a description o…
Harish-Chandra modules for map and affine Lie superalgebras
Lucas Calixto, Vyacheslav Futorny, Henrique Rocha
We obtain a classification of simple modules with finite weight multiplicities over basic classical map superalgebras. Any such module is parabolic induced from a simple cuspidal b…
Integrable bounded weight modules of classical Lie superalgebras at infinity
Lucas Calixto, Ivan Penkov
We classify integrable bounded simple weight modules over classical Lie superalgebras at infinity. We also study the categories of such modules, and we prove that for most of the c…
Local Weyl modules and fusion products for the current superalgebra
Matheus Brito, Lucas Calixto, Tiago Macedo
We study a class of modules, called Chari-Venkatesh modules, for the current superalgebra . This class contains other important modules, such as graded local…