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Jacobi-Trudi Type Formula for Character of Irreducible Representations of $\frak {gl}(m|1)$
Nguyên Luong Thái Bình , Nguyên Thi Phuong Dung , Phùng Hô Hai
Abstract
We prove a determinantal type formula to compute the irreducible characters of the general Lie superalgebra $\mathfrak {gl}(m|1)$ in terms of the characters of the symmetric powers of the fundamental representation and their duals. This formula was conjectured by $J$. van der Jeugt and E. Moens for the Lie superalgebra $\mathfrak {gl}(m|n)$ and generalizes the well-known Jacobi-Trudi formula.