On a determinant formula for some real regular representations

Résumé

We interpret a formula established by Lapid-Mínguez on real regular representations of GLn 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 Uq(slˆk), which are themselves generalizations of the celebrated T-system relations.