University of Sydney Algebra Seminar

Lucas Calixto (University of Minas Gerais)

Friday 6 March, 12-1pm, Place: Carslaw 275

Local Weyl modules and fusion products for the current superalgebra sl(1|2)[t]

We study a class of modules, called Chari-Venkatesh modules, for the current superalgebra sl(1|2)[t]. This class contains other important modules, such as graded local Weyl, truncated local Weyl and Demazure-type modules. We prove that Chari-Venkatesh modules can be realized as fusion products of generalized Kac modules. In particular, this proves a conjecture, that fusion products are independent of their fusion parameters, in the case where the fusion factors are generalized Kac modules. As an application, we obtain bases, dimension and character formulas for Chari-Venkatesh modules.