On a determinant formula for some real regular representations

Abstract

We interpret a formula established by Lapid-M\'ınguez on real regular representations of ${\mathrm{GL}}_n$ 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 $U_q({\widehat{\mathfrak{sl}}}_k)$, which are themselves generalizations of the celebrated $T$-system relations.

21 pages, comments welcome

References in corpus (1)

• Geometric conditions for $\square$-irreducibility of certain representations of the general linear group over a non-archimedean local field