相关论文: Irregular KZ equations and Kac-Moody representatio…
In this work we study Liouville conformal blocks with degenerate primaries and one operator in an irregular representation of the Virasoro algebra. Using an algebraic approach, we derive modified BPZ equations satisfied by such blocks and…
A root of unity limit of the $q$-deformed Virasoro algebra is considered. The $\widehat{sl}(2)_k$ current algebra and the integral formulas of the solutions of the KZ equations can be realized by the $q$-deformed boson at the limit and an…
We study irregular representations of Virasoro algebra associated with half-integer order singularities, which arise naturally in the 2d CFT description of Argyres-Douglas theories of type $(A_1, A_{\text{even}})$ and $(A_1,…
We prove general Dwork-type congruences for Hasse--Witt matrices attached to tuples of Laurent polynomials. We apply this result to establishing arithmetic and $p$-adic analytic properties of functions originating from polynomial solutions…
The goal of this paper is to give a representation-theoretic interpretation of the sine-Gordon equation. We consider a vertex operator representation of affine Kac-Moody algebra \hat{sl_2} on the space of differential operators. In this…
We give a mathematical definition of spaces of irregular vacua/covacua in genus zero, for any simple Lie algebra, working at generic noncritical level. This uses coinvariants of affine-Lie-algebra modules whose parameters match up with…
Motivated by problems arising in the study of N=2 supersymmetric gauge theories we introduce and study irregular singularities in two-dimensional conformal field theory, here Liouville theory. Irregular singularities are associated to…
We consider the subalgebras of split real, non-twisted affine Kac-Moody Lie algebras that are fixed by the Chevalley involution. These infinite-dimensional Lie algebras are not of Kac-Moody type and admit finite-dimensional unfaithful…
These are the notes for a Part III course given in the University of Cambridge in autumn 1998. They contain an exposition of the representation theory of the Lie algebras of compact matrix groups, affine Kac-Moody algebras and the Virasoro…
These lecture notes are a brief introduction to Wess-Zumino-Witten models, and their current algebras, the affine Kac-Moody algebras. After reviewing the general background, we focus on the application of representation theory to the…
Quiver varieties have recently appeared in various different areas of Mathematics such as representation theory of Kac-Moody algebras and quantum groups, instantons on 4-manifolds, and resolutions Kleinian singularities. In this paper, we…
We consider epimorphisms from quantum minimal surface algebras onto involutroy subalgebras of split real simply-laced Kac-Moody algebras and provide examples of affine and finite type. We also provide epimorphisms onto such Kac-Moody…
In this paper we study matrix model realizations of Liouville conformal blocks with degenerate and irregular operators. The corresponding matrix model is Hermitian with a $\beta$-deformed measure and the degree of the potential corresponds…
In this paper we investigate one Wakimoto-type construction of affine Kac-Moody algebras. We obtain a version of the regular representation, on which the affine algebra acts from the left and from the right with the sum of levels equal to…
We introduce an affinization of the quantum Kac-Moody algebra associated to a symmetric generalized Cartan matrix. Based on the affinization, we construct a representation of the quantum Kac-Moody algebra by vertex operators from bosonic…
Affine Kac-Moody algebras give rise to interesting systems of differential equations, so-called Knizhnik-Zamolodchikov equations. The monodromy properties of their solutions can be encoded in the structure of a modular tensor category on (a…
We derive a generalized Knizhnik-Zamolodchikov equation for the correlation function of the intertwiners of the vector and the MacMahon representations of Ding-Iohara-Miki algebra. These intertwiners are cousins of the refined topological…
This paper is to study what we call twisted regular representations for vertex operator algebras. Let $V$ be a vertex operator algebra, let $\sigma_1,\sigma_2$ be commuting finite-order automorphisms of $V$ and let…
We study certain representations of quantum toroidal $\mathfrak{gl}_1$ algebra for $q=t$. We construct explicit bosonization of the Fock modules $\mathcal{F}_u^{(n',n)}$ with a nontrivial slope $n'/n$. As a vector space, it is naturally…
Whenever the group $\R^n$ acts on an algebra $\calA$, there is a method to twist $\cal A$ to a new algebra $\calA_\theta$ which depends on an antisymmetric matrix $\theta$ ($\theta^{\mu \nu}=-\theta^{\nu \mu}=\mathrm{constant}$). The…