Vertex-algebraic structure of principal subspaces of the basic modules for twisted affine Lie algebras of type <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:msubsup><mml:mrow

Penn, Michael; Sadowski, Christopher

doi:10.1016/j.jalgebra.2017.10.022

Cited by 12 publications

(34 citation statements)

References 35 publications

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“…Remark 4.1. We note here that U T L plays the same role that the universal enveloping algebra U (n[ν]) played in in [PS1]- [PS2], [CalMPe], and [CalLM4]. In [P], U L played similar in place of the universal enveloping algebra U (n) from [CLM1]- [CLM2] and [CalLM1]- [CalLM3].…”

Section: 1mentioning

confidence: 99%

“…Remark 2.2. The assumption that N = M = R is quite natural, and the cases studied in [CalLM4], [CalMPe], and [PS1]- [PS2] all satisfy this property. At the end of this work, we present interesting examples in our present setting which also meet this requirement.…”

Section: The Settingmentioning

confidence: 99%

“…We note that certain "commutative" analogues of principal subspaces have been also defined and studied in [T1]- [T3], [J1]- [J2], [JP], [Pr], [P] and others, and quantum analogues have been studied in [Ko1]- [Ko2]. We base our approach in this paper on the vertex-algebraic methods developed in [CLM1]- [CLM2], [CalLM1]- [CalLM4], [S1]- [S2], [C1], and [PS1]- [PS2]. We note that this paper uses many of the techniques developed in these works, but that the principal subspace we study is a twisted analogue of the "commutative" structures mentioned above.…”

Section: Introductionmentioning

confidence: 99%

“…The proof of the completeness of these relations is highly nontrivial, and requires the use of what we call a "generalized Pascal matrix" (see the Appendix for its definition and properties). The remainder of the paper is analogous to [CalLM4], [CalMPe], and [PS1]- [PS2]. We use our presentations to construct exact sequences involving our principal subspace, and use these exact sequences to find a set of recursions satisfied by the multigraded dimension of the principal subspace.…”

Section: Introductionmentioning

confidence: 99%

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Principal subspaces of twisted modules for certain lattice vertex operator algebras

2019

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This is the third in a series of papers studying the vertex-algebraic structure of principal subspaces of twisted modules for lattice vertex operator algebras. We focus primarily on lattices L whose Gram matrix contains only non-negative entries. We develop further ideas originally presented by Calinescu, Lepowsky, and Milas to find presentations (generators and relations) of the principal subspace of a certain natural twisted module for the vertex operator algebra V L . We then use these presentations to construct exact sequences involving this principal subspace, which give a set of recursions satisfied by the multigraded dimension of the principal subspace and allow us to find the multigraded dimension of the principal subspace. and D(1) 4 , Glas. Mat. Ser. III 46, 66 (2011), 49-70.

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Section: 1mentioning

confidence: 99%

Section: The Settingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Principal subspaces of twisted modules for certain lattice vertex operator algebras

2019

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“…The virtual subspaces are analogous to the principal-like subspaces in the untwisted case introduced in [CalLM3]. These subspaces were implicitly used in the proof of all other twisted results, [CalLM4], [CMP], [PS1]- [PS2], and [PSW], but the increase in the complexity of the current setting requires that these spaces to be worked with explicitly.…”

Section: Introductionmentioning

confidence: 99%

Presentations of Principal Subspaces of Higher Level Standard A2(2)${A}_{2}^{(2)}$-Modules

Calinescu

Penn

Sadowski

2018

Algebr Represent Theor

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We study the principal subspaces of higher level standard A(2) 2modules, extending earlier work in the level one case, by Calinescu, Lepowsky and Milas. We prove natural presentations of principal subspaces and also of certain related spaces. By using these presentations we obtain exact sequences, which yield recursions satisfied by the characters of the principal subspaces and related spaces. We conjecture a formula for a specialized character of the principal subspace, given by the Nahm sum of the inverse of the tadpole Cartan matrix.

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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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Vertex-algebraic structure of principal subspaces of the basic modules for twisted affine Lie algebras of type A2n−1(2),

Cited by 12 publications

References 35 publications

Principal subspaces of twisted modules for certain lattice vertex operator algebras

Principal subspaces of twisted modules for certain lattice vertex operator algebras

Presentations of Principal Subspaces of Higher Level Standard A2(2)${A}_{2}^{(2)}$-Modules

Quasi-particle Bases of Principal Subspaces of Affine Lie Algebras

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