The structure of standard modules, I: Universal algebras and the Rogers-Ramanujan identities

Lepowsky, James; Wilson, Robert Lee

doi:10.1007/bf01388447

Cited by 241 publications

(170 citation statements)

References 29 publications

(58 reference statements)

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“…Additional evidence for this connection for higher-rank cases can be found in the ongoing work [3]. We remark here that there is a well-known and very important connection between the representation theory of level 123 one representations and number theory through the Rogers-Ramanujan identities [15]. But this does not appear to be related in any obvious way to our study of Demazure flags.…”

Section: Introductionmentioning

confidence: 70%

Demazure flags, q-Fibonacci polynomials and hypergeometric series

2018

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We study a family of finite-dimensional representations of the hyperspecial parabolic subalgebra of the twisted affine Lie algebra of type A (2) 2 . We prove that these modules admit a decreasing filtration whose sections are isomorphic to stable Demazure modules in an integrable highest weight module of sufficiently large level. In particular, we show that any stable level m Demazure module admits a filtration by level m Demazure modules for all m ≥ m . We define the graded and weighted generating functions which encode the multiplicity of a given Demazure module and establish a recursive formulae. In the case when m = 1, 2 and m = 2, 3, we determine these generating functions completely and show that they define hypergeometric series and that they are related to the q-Fibonacci polynomials defined by Carlitz.

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Section: Introductionmentioning

confidence: 70%

Demazure flags, q-Fibonacci polynomials and hypergeometric series

2018

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“…Using the Z -algebra introduced and studied in [19] and [20,21], we can rewrite ω α and W 3 α in terms of Z -operators Z α (m) and Z −α (n). It is not too hard to see that…”

Section: Vertex Operator Algebra N(g K)mentioning

confidence: 99%

“…The parafermion algebra was first studied in [27] in the context of conformal field theory. It was clarified in [7] that the parafermion algebras are essentially the Z -algebras introduced and studied earlier in [19][20][21] in the process of studying the representation theory for the affine Kac-Moody Lie algebras. As it proved in [7], the parafermion algebras generate certain generalized vertex operator algebras.…”

Section: Introductionmentioning

confidence: 99%

The Structure of Parafermion Vertex Operator Algebras: General Case

Dong

Lam

Wang

et al. 2010

Commun. Math. Phys.

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“…There exist several constructions of monomial bases in terms of the chiral conformal algebras (the Virasoro algebra, the affine Lie algebras, and so on), instead of the intertwiners [3,4,5,6]. For comparison we review one of such constructions for the Virasoro algebra.…”

Section: Introductionmentioning

confidence: 99%

A Monomial Basis for the Virasoro Minimal Series M(p,p′) : The Case 1<p′/p<2

Feigin

Jimbo

Miwa

et al. 2005

Commun. Math. Phys.

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Abstract. Quadratic relations of the intertwiners are given explicitly in two cases of chiral conformal field theory, and monomial bases of the representation spaces are constructed by using the Fourier components of the intertwiners. The two cases are the (p, p ′ )-minimal series Mr,s (1 ≤ r ≤ p − 1, 1 ≤ s ≤ p ′ − 1) for the Virasoro algebra where 1 < p ′ /p < 2, and the level k integrable highest weight modules V (λ) (0 ≤ λ ≤ k) for the affine Lie algebra sl2.

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The structure of standard modules, I: Universal algebras and the Rogers-Ramanujan identities

Cited by 241 publications

References 29 publications

Demazure flags, q-Fibonacci polynomials and hypergeometric series

Demazure flags, q-Fibonacci polynomials and hypergeometric series

The Structure of Parafermion Vertex Operator Algebras: General Case

A Monomial Basis for the Virasoro Minimal Series M(p,p′) : The Case 1<p′/p<2

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