A filtration on the ring of Laurent polynomials and representations of the general linear Lie algebra

26 Jun 2018  ·  Choi Cheonho, Kim Sangjib, Seo HaeYun ·

We first present a filtration on the ring L of Laurent polynomials such that the direct sum decomposition of its associated graded ring gr L agrees with the direct sum decomposition of gr L, as a module over the complex general linear Lie algebra gl(n), into its simple submodules. Next, generalizing the simple modules occurring in gr L, we give some explicit constructions of weight multiplicity-free irreducible representations of gl(n)...

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Representation Theory Commutative Algebra