Super-immanants and Littlewood correspondences

Fuente: arXiv
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Autores principales: Jing, Naihuan, Liu, Yinlong, Zhang, Jian
Formato: Preprint
Publicado: 2026
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author Jing, Naihuan
Liu, Yinlong
Zhang, Jian
author_facet Jing, Naihuan
Liu, Yinlong
Zhang, Jian
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2603_21893
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Super-immanants and Littlewood correspondences
Jing, Naihuan
Liu, Yinlong
Zhang, Jian
Representation Theory
Combinatorics
Quantum Algebra
Primary: 17A70 Secondary: 17B35, 15A15, 05E05, 05E10
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.
title Super-immanants and Littlewood correspondences
topic Representation Theory
Combinatorics
Quantum Algebra
Primary: 17A70 Secondary: 17B35, 15A15, 05E05, 05E10
url https://arxiv.org/abs/2603.21893