Quantum supersymmetric pairs of basic types

2024/08/06 by Yaolong Shen, Weiqiang Wang, Shen, Yaolong +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Quantum Mechanics and Non-Hermitian Physics #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2408.02874

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 K-matrix associated with the quantum supersymmetric pairs. We also formulate a Schur duality between an \imathquantum supergroup (which is a new q-deformation of an ortho-symplectic Lie superalgebra) and the q-Brauer algebra.

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