Characters of Feigin-Stoyanovsky's type subspaces of level one modules for affine Lie algebras of types Al(1) and D4(1)

Trupčević, Goran

doi:10.3336/gm.46.1.08

Cited by 11 publications

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“…) and gr(W ′ Λ1,0 ). Similarly we can also prove the isomorphism in cases where ω = ω i , 2 ≤ i ≤ n by making use of [Tru11,(3.21)]. 5.3.…”

Section: Feigin-stoyanovsky Type Subspacesmentioning

confidence: 90%

“…In [Pri94,Pri00], M.Primc studied Feigin-Stoyanovsky type subspaces which are analogs of principal subspaces but easier to analyze. They are further investigated for many integral levels and types [BPT16,Jer12,Tru09,Tru11]. Here we follow notation from [MP12] where principal subspaces are defined for general integral lattices (not necessarily positive definite).…”

Section: Principal Subspacesmentioning

confidence: 99%

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Some remarks on associated varieties of vertex operator superalgebras

2020

Preprint

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We study several families of vertex operator superalgebras from a jet (super)scheme point of view. We provide new examples of vertex algebras which are "chiralizations" of their Zhu's Poisson algebras R V . Our examples come from affine C(1) ℓ -series vertex algebras (ℓ ≥ 1), certain N = 1 superconformal vertex algebras, Feigin-Stoyanovsky principal subspaces, Feigin-Stoyanovsky type subspaces, graph vertex algebras W Γ , and extended Virasoro vertex algebra. We also give a counterexample to the chiralization property for the N = 2 superconformal vertex algebra of central charge 1.

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“…) and gr(W ′ Λ1,0 ). Similarly we can also prove the isomorphism in cases where ω = ω i , 2 ≤ i ≤ n by making use of [Tru11,(3.21)]. 5.3.…”

Section: Feigin-stoyanovsky Type Subspacesmentioning

confidence: 90%

Section: Principal Subspacesmentioning

confidence: 99%

Some remarks on associated varieties of vertex operator superalgebras

2020

Preprint

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Quasi-particle Bases of Principal Subspaces of Affine Lie Algebras

Butorac

2019

Springer INdAM Series

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Generalizing our earlier work, we construct quasi-particle bases of principal subspaces of standard module L X (1) l (kΛ 0 ) and generalized Verma module N X (1) l (kΛ 0 ) at level k ≥ 1 in the case of affine Lie algebras of types B(1) l and C (1) l . As a consequence, from quasi-particle bases, we obtain the graded dimensions of these subspaces. IntorductionLet g be a simple complex Lie algebra of type X l , with a Cartan subalgebra h, the set of simple roots Π = {α 1 , . . . , α l } and the triangular decomposition g = n − ⊕ h ⊕ n + , where n + is a direct sum of its one dimensional subalgebras corresponding to the positive roots. Denote by L(n + ) a subalgebra of untwisted affine Lie algebra g of type X(1) lLet V be a highest g-module with highest weight Λ and highest weight vector v Λ . We define the principal subspace W V of V asIn this paper we study principal subspaces of the generalized Verma module N X (1) l (kΛ 0 ) and its irreducible quotient L X (1) l (kΛ 0 ) at level k ≥ 1, defined over the affine Lie algebras of type B(1) l and C(1) l . The study of principal subspaces of standard (i.e., integrable highest weight) modules of the simply laced affine Lie algebras and its connection to Rogers-Ramanujan identities was initiated in the work of B. L. Feigin and A. V. Stoyanovsky [FS] and has been further developed in [AKS]

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