2020
DOI: 10.1080/00927872.2020.1788046
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A note on principal subspaces of the affine Lie algebras in types Bl(1),Cl(1),F4(1) and G2(1)

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Cited by 6 publications
(14 citation statements)
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“…where e µ denote the Weyl group translation operators parametrized by the elements of the coroot lattice Q ∨ of the simple Lie algebra g, the set B U ( h − ) is the Poincaré-Birkhoff-Witt-type basis of the universal enveloping algebra U( h − ) and B ′ W L(Λ) is a certain subset of B W L(Λ) . We verify that set (2) spans L(Λ) by using the relations among quasiparticles and arguing as in [Bu1,Bu2,Bu3,Bu5,BK]. On the other hand, our proof of linear independence relies on generalizing Georgiev's arguments originated in [G1] to standard modules for all untwisted affine Lie algebras.…”
Section: Introductionmentioning
confidence: 88%
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“…where e µ denote the Weyl group translation operators parametrized by the elements of the coroot lattice Q ∨ of the simple Lie algebra g, the set B U ( h − ) is the Poincaré-Birkhoff-Witt-type basis of the universal enveloping algebra U( h − ) and B ′ W L(Λ) is a certain subset of B W L(Λ) . We verify that set (2) spans L(Λ) by using the relations among quasiparticles and arguing as in [Bu1,Bu2,Bu3,Bu5,BK]. On the other hand, our proof of linear independence relies on generalizing Georgiev's arguments originated in [G1] to standard modules for all untwisted affine Lie algebras.…”
Section: Introductionmentioning
confidence: 88%
“…Proof. We prove linear independence of the spanning set B L(Λ) by slightly modifying the arguments in [Bu1,Bu2,Bu3,Bu5,BK]. We consider a finite linear combination of vectors in B L(Λ) ,…”
Section: The Main Theorem Consider the Decompositionmentioning
confidence: 99%
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