On the faces of the tensor cone of symmetrizable Kac-Moody lie algebras

arXiv1902.02049MaRDI QIDQ6503421

Author name not available (Why is that?)

Abstract: In this paper, we are interested in the decomposition of the tensor product of two representations of a symmetrizable Kac-Moody Lie algebra g, and more precisely in the tensor cone of g. Let P + be the set of dominant integral weights. For $lambda$ $in$ P + , L($lambda$) denotes the (irreducible) integrable, highest weight representation of g with highest weight $lambda$. Let P +,Q be the rational convex cone generated by P +. Consider the tensor cone $Gamma$(g) := {($lambda$ 1 , $lambda$ 2 , $mu$) $in$ P 3 +,Q : $exists$N $ge$ 1 such that L(N$mu$) $subset$ L(N$lambda$ 1)$otimes$L(N$lambda$ 2)}. If g is finite dimensional, $Gamma$(g) is a polyhedral convex cone described in [BK06] by an explicit finite list of inequalities. In [Res10] this list of inequalities is proved to be irredundant: each inequality corresponds to a codimension one face. In general, $Gamma$(g) is neither polyhedral, nor closed. Brown-Kumar [BK14] obtained a list of inequalities that describe $Gamma$(g) conjecturally. Here, we prove that each of Brown-Kumar's inequalities corresponds to a codimension one face of $Gamma$(g).

This page was built for publication: On the faces of the tensor cone of symmetrizable Kac-Moody lie algebras

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6503421)