Jacobi-Trudi type formula for a class of irreducible representations of \frakgl(m|n)

2020/01/14 by Nguyên Luong Thái Bình, Binh, Nguyen Luong Thai
Mathematics · Physics and Astronomy · #17B10 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2001.04679

openalex publication_date 2020/01/14 · openalex created_date 2020/01/23 · openalex updated_date 2026/07/28

Abstract

We prove a determinantal type formula to compute the characters for a class of irreducible representations of the general Lie superalgebra \mathfrakgl(m|n) 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 and was generalized the well-known Jacobi-Trudi formula.

Related

• Combinatorics of irreducible characters for Lie superalgebra \frakgl(m,n)
• Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra gl(m|n)
• Factorial characters of classical Lie groups and their combinatorial realisations
• Calculation of 6j-symbols for the Lie algebra \mathfrakgl_n
• Gruson-Serganova character formulas and the Duflo-Serganova cohomology functor