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Some branching formulas for Kac--Moody Lie algebras
In this paper we give some branching rules for the fundamental
representations of Kac--Moody Lie algebras associated to -shaped graphs.
These formulas are useful to describe generators of the generic rings for free
resolutions of length three described in [JWm16]. We also make some conjectures
about the generic rings
Young tableaux, canonical bases and the Gindikin-Karpelevich formula
A combinatorial description of the crystal B(infinity) for finite-dimensional
simple Lie algebras in terms of certain Young tableaux was developed by J. Hong
and H. Lee. We establish an explicit bijection between these Young tableaux and
canonical bases indexed by Lusztig's parametrization, and obtain a
combinatorial rule for expressing the Gindikin-Karpelevich formula as a sum
over the set of Young tableaux.Comment: 19 page
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