Quantum supersymmetric pairs of basic types
Quantum Algebra
2025-08-25 v2 Representation Theory
Abstract
We formulate and classify super Satake diagrams under a mild assumption, building on arbitrary Dynkin diagrams for finite-dimensional basic Lie superalgebras. We develop a theory of quantum supersymmetric pairs associated to the super Satake diagrams. We establish the quantum Iwasawa decomposition and construct quasi -matrix associated with the quantum supersymmetric pairs. We also formulate a Schur duality between an quantum supergroup (which is a new -deformation of an ortho-symplectic Lie superalgebra) and the -Brauer algebra.
Cite
@article{arxiv.2408.02874,
title = {Quantum supersymmetric pairs of basic types},
author = {Yaolong Shen and Weiqiang Wang},
journal= {arXiv preprint arXiv:2408.02874},
year = {2025}
}
Comments
44 pages, 4 tables, many diagrams; v2, 47 pages, major revision, corrected mistakes including Table 3, reference updated