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Acta Mathematica Vietnamica

Jacobi-Trudi Type Formula for Character of Irreducible Representations of 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 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 gl(m|n) and generalizes the well-known Jacobi-Trudi formula.