Super-immanants and Littlewood correspondences
Representation Theory
2026-03-24 v1 Combinatorics
Quantum Algebra
Abstract
In this paper, we introduce the notion of super-immanants for supermatrices over a supercommutative algebra. Using the super Schur-Weyl duality we show that the super immanants play a significant role in covariant tensor representations of the general linear Lie superalgebra. Among various things, we obtain a supertrace formula for super-immanants, which generalizes Kostant's trace formula to the super setting. Furthermore, we show that the Littlewood correspondences between super-immanants and supersymmetric polynomials establish an isomorphism between their corresponding algebras.
Keywords
Cite
@article{arxiv.2603.21893,
title = {Super-immanants and Littlewood correspondences},
author = {Naihuan Jing and Yinlong Liu and Jian Zhang},
journal= {arXiv preprint arXiv:2603.21893},
year = {2026}
}
Comments
28 pp