Lattice Vertex Superalgebras, I: Presentation of the Principal Subalgebra

Penn, Michael

doi:10.1080/00927872.2012.714024

Cited by 14 publications

(6 citation statements)

References 27 publications

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“…Andrews-Gordon identities). More recently, Nahm sums have appeared in several areas including vertex algebras [26,33,37,40], DAHA [18], wall-crossing phenomena and quivers [17,28,34], in connection to colored HOMFLY-PT polynomials [29], and in formulas for the "tail" of colored Jones polynomials [9,22,27].…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

“…As explained in Section 2, for a given graph Γ, there is a graded commutative algebra J ∞ (R), the ring of functions of the infinite jet scheme X ∞ , where X = Spec(R), whose Hilbert series is given by (1.2). This infinitely-generated algebra is closely related to a certain principal subspace vertex algebra constructed from the adjacency matrix of Γ [26,33,37,40], in the sense that its character is the Hilbert series of J ∞ (R).…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

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Graph Schemes, Graph Series, and Modularity

Bringmann¹,

Jennings-Shaffer²,

Milas³

2021

Preprint

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To a simple graph we associate a so-called graph series, which can be viewed as the Hilbert-Poincaré series of a certain infinite jet scheme. We study new q-representations and examine modular properties of several examples including Dynkin diagrams of finite and affine type. Notably, we obtain new formulas for graph series of type A7 and A8 in terms of "sum of tails" series, and of type D4 and D5 in the form of indefinite theta functions of signature (1, 1). We also study examples related to sums of powers of divisors corresponding to 5-cycles. For several examples of graphs, we prove that graph series are so-called mixed quantum modular forms.

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Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

Graph Schemes, Graph Series, and Modularity

Bringmann¹,

Jennings-Shaffer²,

Milas³

2021

Preprint

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“…We assume that a has the minimum weight among all elements that satisfy above conditions. Again from the same argument from [Pen14], this a can be written as ux r (−1) where…”

Section: Feigin-stoyanovsky Type Subspacesmentioning

confidence: 99%

“…We prove the case when α, α = 0. For other cases, it is proved in [Pen14]. Firstly we define a map e αr : W Γ → W Γ as e αr ((e αj ) (m) 1) = (e αj ) (m) (e αr ) (−1) 1.…”

Section: Feigin-stoyanovsky Type Subspacesmentioning

confidence: 99%

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 the knowledge of presentation presents an important question in this study ([6], [7], [8], [9], [27], [23]).…”

Section: B Feigin and A Stoyanovsky Introduced Principal Subspaces Of...mentioning

confidence: 99%