Related papers: Free Field Realizations of Superelliptic Affine Li…
The minimal model $\mathfrak{osp}(1|2)$ vertex operator superalgebras are the simple quotients of affine vertex operator superalgebras constructed from the affine Lie super algebra $\widehat{\mathfrak{osp}}(1|2)$ at certain rational values…
We investigate the free fields realization of the twisted Heisenberg-Virasoro algebra $\mathcal{H}$ at level zero. We completely describe the structure of the associated Fock representations. Using vertex-algebraic methods and screening…
In this paper, we study the representation theory for the affine Lie algebra $\H$ associated to the Nappi-Witten model $H_{4}$. We classify all the irreducible highest weight modules of $\H$. Furthermore, we give a necessary and sufficient…
We study a free field realization of the elliptic quantum algebra $U_{q,p}(sl_3^)$ for arbitrary level $k$. We give the free field realization of elliptic analogue of Drinfeld current associated with $U_{q,p}(sl_3^)$ for arbitrary level…
We develop some basic properties such as $p$-centers of affine vertex algebras and free field vertex algebras in prime characteristic. We show that the Wakimoto-Feigin-Frenkel homomorphism preserves the $p$-centers by providing explicit…
We construct a free field realization of the elliptic quantum algebra $U_{q,p}(\hat{sl_N})$ for arbitrary level $k \neq 0,-N$. We study Drinfeld current and the screening current associated with $U_{q,p}(\hat{sl_N})$ for arbitrary level…
We study the quantum $N=2$ super-$W_{3}$ algebra using the free field realization, which is obtained from the supersymmetric Miura transformation associated with the Lie superalgebra $A(2|1)$. We compute the full operator product expansions…
In this review, we study free field realizations of the Feigin-Odesskii algebra. We construct free field realizations of a pair of infinitely many commutative operators, associated with the elliptic quantum group $U_{q,p}(\widehat{sl_N})$.
In this paper free field realizations of affine current superalgebras are considered. Based on quantizing differential operator realizations of the corresponding basic Lie superalgebras, general and simple expressions for both the bosonic…
We generalize Feigin and Miwa's construction of extended vertex operator (super)algebras $A_{k}(sl(2))$ for other types of simple Lie algebras. For all the constructed extended vertex operator (super)algebras, irreducible modules are…
We present a general vertex operator construction based on the Fock space for an affine Lie algebras of type $A$. This construction allows us to give a unified treatment for both the homogeneous and principle realizations of the affine Lie…
We construct Wakimoto modules for twisted affine Lie algebras, and interpret the construction in terms of vertex algebras and their twisted modules. Using the Wakimoto realization, we prove the Kac-Kazhdan conjecture on the characters of…
We study the boundary vertex algebras of $A$-twisted $\mathcal{N}=4$ Abelian gauge theories in three dimensions. These are identified with the BRST quotient (semi-infinite cohomology) of collections of symplectic bosons and free fermions…
The orbifold construction $A\mapsto A^G$ for a finite group $G$ is fundamental in rational conformal field theory. The construction of $Rep(A^G)$ from $Rep(A)$ on the categorical level, often called gauging, is also prominent in the study…
Wakimoto modules are representations of affine Kac-Moody algebras in Fock modules over infinite-dimensional Heisenberg algebras. In these lectures we present the construction of the Wakimoto modules from the point of view of the vertex…
We present a new application of affine Lie algebras to massive quantum field theory in 2 dimensions, by investigating the $q\to 1$ limit of the q-deformed affine $\hat{sl(2)}$ symmetry of the sine-Gordon theory, this limit occuring at the…
It is well known that the bosonized version of the Wakimoto construction allows the explicit realization of any affine algebra $\widehat{g}$, with arbitrary level $k$ in the homogeneous gradation, in terms of $dim(g)$ free bosonic fields.…
Certain integrable hierarchies appearing in random matrix theory, enumerative geometry, and conformal field theory are governed by Virasoro/$W$-algebra constraints and their $W$-representations.Motivated by the Gaussian Hermitian…
Using the invariant theory of arc spaces, we find minimal strong generating sets for certain cosets of affine vertex algebras inside free field algebras that are related to classical Howe duality. These results have several applications.…
We construct a realization of the elliptic quantum algebra $U_{q,p}(\hat{sl_N})$ for any given level $k$ in terms of free boson fields and their twisted partners. It can be considered as the elliptic deformation of the Wakimoto realization…