Stabilization Phenomena in Kac-moody Algebras and Quiver Varieties
نویسنده
چکیده
Let X be the Dynkin diagram of a symmetrizable Kac-Moody algebra, and X0 a subgraph with all vertices of degree 1 or 2. Using the crystal structure on the components of quiver varieties for X , we show that if we expand X by extending X0, the branching multiplicities and tensor product multiplicities stabilize, provided the weights involved satisfy a condition which we call “depth” and are supported outside X0. This extends a theorem of Kleber and Viswanath. Furthermore, we show that the weight multiplicities of such representations are polynomial in the length of X0, generalizing the same result for Al by Benkart, et al.
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