Related papers: Virasoro Representations on (Diff S1)/S1 Coadjoint…
We construct and discuss the Fock-space representation for a deformed oscillator with "peculiar" statistics. We show that corresponding algebra represents deformed supersymmetric oscillator.
We identify the algebra of matrix elements of big projective modules in category O with the regular functions on the big Bruhat cell of G. Analogous extensions of the regular representations of the affine Lie and Virasoro algebras yield…
We consider exceptional vertex operator algebras for which particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendants of the vacuum. We discuss constraints on these theories that…
Concerning the new boson representation presented in Part I, it is proved that this representation obeys the su(2)-algebra in a certain subspace in the whole boson space constructed by the Schwinger boson representation of the…
We investigate the structure of representations of the (positive half of the) Virasoro algebra and situations in which they decompose as a tensor product of Lie algebra representations. As an illustration, we apply these results to the…
This article is concerned with an extensive study of an infinite-dimensional Lie algebra $\mathfrak{sv}$, introduced in the context of non-equilibrium statistical physics, containing as subalgebras both the Lie algebra of invariance of the…
Chiral edges of 2+1D systems can have very robust emergent conformal symmetry. When the edge is purely chiral, the Hilbert space of low-energy edge excitations can form a representation of a single Virasoro algebra. We propose a method to…
The Virasoro groups are a family of central extensions of $\mathrm{Diff}^+(S^1)$, the group of orientation-preserving diffeomorphisms of $S^1$, by the circle group $\mathbb T$. We give a novel, geometric construction of these central…
Using the language of vertex operator algebras (VOAs) and vector-valued modular forms we study the modular group representations and spaces of 1-point functions associated to intertwining operators for Virasoro minimal model VOAs. We…
Associated varieties are geometric objects appearing in infinite-dimensional representations of semisimple Lie algebras (groups). By applying Fourier transformations to the natural orthogonal oscillator representations of special linear Lie…
In this paper, we classify all irreducible weight modules with finite-dimensional weight spaces over the affine-Virasoro Lie algebra of type $A_1$.
We present the list of irreducible (generalized) highest weight modules over the Virasoro algebra and N=1 super-Virasoro algebras obtained as factor-modules of (generalized) Verma modules. We present also the character formulae of all these…
We discuss some aspects of the representation theory of the deformed Virasoro algebra $\virpq$. In particular, we give a proof of the formula for the Kac determinant and then determine the center of $\virpq$ for $q$ a primitive N-th root of…
SW(3/2,2) superconformal algebra is W algebra with two Virasoro operators. The Kac determinant is calculated and the complete list of unitary representations is determined. Two types of extensions of SW(3/2,2) algebra are discussed. A new…
We present sum representations for all characters of the unitary Virasoro minimal models. They can be viewed as fermionic companions of the Rocha-Caridi sum representations, the latter related to the (bosonic) Feigin-Fuchs-Felder…
This work concerns the representation theory of the affine Lie algebra $A_1^{(1)}$ at fractional level and its links to the representation theory of the Virasoro algebra. We introduce affine Kac modules as certain finitely generated…
We propose a series representation for the Virasoro fusion and modular kernels at any irrational central charge. Two distinct, yet closely related formulas are needed for the cases $c\in \mathbb C \backslash (-\infty,1]$ and $c <1$. Our…
We present a unified framework for the holographic computation of Virasoro conformal blocks at large central charge. In particular, we provide bulk constructions that correctly reproduce all semiclassical Virasoro blocks that are known…
We review the holomorphic block factorisation of partition functions of supersymmetric theories on compact manifolds in various dimensions. We then show how to interpret 3d and 5d partition functions as correlation functions with underlying…
It has long been known that the moduli space of hyperbolic metrics on the disc can be identified with the Virasoro coadjoint orbit $\mathrm{Diff}^+(S^1) / \mathrm{SL}(2,\mathbb{R})$. The interest in this relationship has recently been…