On a determinant formula for some real regular representations

2023/01/02 by Léa Bittmann, Bittmann, Léa
Mathematics · #Algebraic structures and combinatorial models #Advanced Algebra and Geometry #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2301.00784

Abstract

We interpret a formula established by Lapid-M'ınguez on real regular representations of \rm GL_n over a local non-archimedean field as a matrix determinant. We use the Lewis Carroll determinant identity to prove new relations between real regular representations. Through quantum affine Schur-Weyl duality, these relations generalize Mukhin-Young's Extended T-systems, for representations of the quantum affine algebra U_q(\widehat\mathfraksl_k), which are themselves generalizations of the celebrated T-system relations.

Related

• Finite Dimensional Representations of Quantum Affine Algebras
• Determinants in Quantum Matrix Algebras and Integrable Systems
• Quantum determinants
• RE-algebras, quasi-determinants and the full Toda system
• Embeddings among quantum affine \mathfraksl_n