On Classical groups detected by the triple tensor product and the Littlewood–Richardson semigroup

摘要

Langlands’ beyond endoscopy proposal for establishing functoriality motivates the study of irreducible subgroups of $$mathrm {GL}_n$$ GL n that stabilize a line in a given repesentation of $$mathrm {GL}_n$$ GL n . Such subgroups are said to be detected by the representation. In this paper we continue our study of the important special case where the representation of $$mathrm {GL}_n$$ GL n is the triple tensor product representation $$otimes ^3$$ ? 3 . We prove a family of results describing when subgroups isomorphic to classical groups of type $$B_{n}$$ B n , $$C_n$$ C n , $$D_{2n}$$ D 2 n are detected.