Light ladders and clasp conjectures

By Ben Elias. 2015

47 citations recorded by the source corpus.

Morphisms between tensor products of fundamental representations of the quantum group of sl(n) are described by the sl(n)-webs of Cautis-Kamnitzer-Morrison. Using these webs, we provide an explicit, root-theoretic formula for the local intersection forms attached to each summand of the tensor product of an irreducible representation with a fundamental representation. We prove this formula for n at most 4, and conjecture that it holds for all n. Given two sequences of fundamental weights which sum to the same dominant weight, the clasp is the morphism between the corresponding tensor products which projects to the top indecomposable summand. Using our computation of intersection forms, we provide a recursive, ``triple-clasp expansion'' formula for clasps. In addition, we describe the cellular structure on sl(n)-webs, and prove that sl(n)-webs are an integral form for tilting modules of quantum groups.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ecc13414f9aef11a361a32227635935a8b0d3baa

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Semi-Infinite Highest Weight Categories (2018, methodology): “nsion of the path algebra A of Aop which is an upper ﬁnite based quasi-hereditary algebra. We expect that an explicit idempotent-adapted cellular basis for A could be constructed using the methods of [Eli]. The general principles outlined so far are valid also when G is replaced by the corresponding”