Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras

Kač, Victor G.; Raina, A.K.

doi:10.1142/8882

Cited by 261 publications

(244 citation statements)

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“…We sometimes present more material than we will need when doing so will help aid intuition. More detailed presentations of the infinite wedge include [Oko01], [KR87], and [MJD00].…”

Section: The Infinite Wedgementioning

confidence: 99%

Double Hurwitz numbers via the infinite wedge

Johnson

2015

Trans. Amer. Math. Soc.

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Abstract. We derive an algorithm to produce explicit formulas for certain generating functions of double Hurwitz numbers. These formulas generalize a formula in [GJV05] for one part double Hurwitz numbers. Immediate consequences include a new proof that double Hurwitz numbers are piecewise polynomial, an understanding of the chamber structure and wall crossing for these polynomials, and a proof of the Strong Piecewise Polynomiality conjecture ofThe method is a straightforward application of Okounkov's expression [Oko00] for double Hurwitz numbers in terms of operators on the infinite wedge. We begin with a introduction to the infinite wedge tailored to our use.

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“…We sometimes present more material than we will need when doing so will help aid intuition. More detailed presentations of the infinite wedge include [Oko01], [KR87], and [MJD00].…”

Section: The Infinite Wedgementioning

confidence: 99%

Double Hurwitz numbers via the infinite wedge

Johnson

2015

Trans. Amer. Math. Soc.

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“…The notion of a vertex algebra introduced by Borcherds [9] provides a rigorous algebraic description of two-dimensional chiral conformal field theory [8,12,26], and is a powerful tool for studying representations of infinitedimensional Lie algebras [31,35]. We will assume that the reader is familiar with the theory of vertex algebras as presented in [32] (see also [23,24,35,44] for other sources).…”

Section: Introductionmentioning

confidence: 99%

“…We will assume that the reader is familiar with the theory of vertex algebras as presented in [32] (see also [23,24,35,44] for other sources). Given an automorphism ϕ of a vertex algebra V , one considers the so-called ϕ-twisted V -modules [5,14,21,24], which are useful for constructing modules of the orbifold subalgebra consisting of elements fixed by ϕ (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Twisted logarithmic modules of free field algebras

Bakalov

Sullivan

2016

Journal of Mathematical Physics

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Abstract. Given a non-semisimple automorphism ϕ of a vertex algebra V , the fields in a ϕ-twisted V -module involve the logarithm of the formal variable, and the action of the Virasoro operator L0 on such module is not semisimple. We construct examples of such modules and realize them explicitly as Fock spaces when V is generated by free fields. Specifically, we consider the cases of symplectic fermions (odd superbosons), free fermions, and βγ-system (even superfermions). In each case, we determine the action of the Virasoro algebra.

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“…As it is well-known that the Virasoro algebra is an important object in mathematics and physics, whose theory has been widely used in literature (e.g., [2,3]). Various generalizations of the Virasoro algebra have been studied by several authors (e.g., [3][4][5][8][9][10][11][12]).…”

Section: Introductionmentioning

confidence: 99%

“…Various generalizations of the Virasoro algebra have been studied by several authors (e.g., [3][4][5][8][9][10][11][12]). In this paper, (1+t) i , a ∈ Γ, i ∈ Z + .…”

Section: Introductionmentioning

confidence: 99%