Generalised spherical minors and their relations

Abstract

Let H be a spherical subgroup of minimal rank of the semisimple simply connected complex algebraic group G. We define some functions on the homogeneous space G/H that we call generalised spherical minors. When G = H x H, we recover Fomin-Zelevinsky generalised minors. We prove that generalised spherical minors satisfy some integer coefficients polynomial relations, that extend the identities of classical generalised minors due to Fomin and Zelevinsky, and that have the shape of exchange relations of LP-algebras.