Representations of Hecke-Clifford superalgebras at roots of unity

Fuente: arXiv
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Main Authors: Chen, Minjia, Wan, Jinkui
Format: Preprint
Published: 2026
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author Chen, Minjia
Wan, Jinkui
author_facet Chen, Minjia
Wan, Jinkui
contents In this article, we give a classification of irreducible completely splittable representations of affine Hecke-Clifford superalgebras $H_n^{\mathrm{aff}}(q)$ when $q^2$ is a primitive $h$-th root of unity. As an application, we derive a necessary and sufficient condition for the finite Hecke-Clifford superalgebra $H_n(q)$ to be semisimple. Specially we show that $H_n(q)$ is semisimple if and only $h >n$ in the case $h$ is odd and $h >2n$ in the case $h$ is even.
format Preprint
id arxiv_https___arxiv_org_abs_2605_11778
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Representations of Hecke-Clifford superalgebras at roots of unity
Chen, Minjia
Wan, Jinkui
Representation Theory
Combinatorics
20C08, 05E10, 17B10
In this article, we give a classification of irreducible completely splittable representations of affine Hecke-Clifford superalgebras $H_n^{\mathrm{aff}}(q)$ when $q^2$ is a primitive $h$-th root of unity. As an application, we derive a necessary and sufficient condition for the finite Hecke-Clifford superalgebra $H_n(q)$ to be semisimple. Specially we show that $H_n(q)$ is semisimple if and only $h >n$ in the case $h$ is odd and $h >2n$ in the case $h$ is even.
title Representations of Hecke-Clifford superalgebras at roots of unity
topic Representation Theory
Combinatorics
20C08, 05E10, 17B10
url https://arxiv.org/abs/2605.11778