## 18 Citations

𝕁-Intermediate Wakimoto Modules

- Mathematics
- 2013

In this article we construct certain free field realizations of the affine Lie algebras that depend on a fixed subset 𝕁 of N* and a parameter r, 0 ≤ r ≤ n. For r = 0 our construction generalizes the…

A WAKIMOTO TYPE REALIZATION OF TOROIDAL

- Mathematics
- 2010

The authors construct a Wakimoto type realization of toroidal sln+1 The representation constructed in this paper utilizes non-commuting differential operators acting on the tensor product of two…

A Wakimoto Type Realization of Toroidal 𝔰𝔩n+1

- Mathematics
- 2012

The authors construct a Wakimoto type realization of toroidal 𝔰𝔩n+1. The representation constructed in this paper utilizes non-commuting differential operators acting on the tensor product of two…

Generalized Imaginary Verma and Wakimoto modules

- Mathematics
- 2022

. We develop a general technique of constructing new irreducible weight modules for any aﬃne Kac-Moody algebra using the parabolic induction, in the case when the Levi factor of a parabolic…

Localization of Free Field Realizations of Affine Lie Algebras

- Mathematics
- 2014

We use localization technique to construct new families of irreducible modules of affine Kac–Moody algebras. In particular, localization is applied to the first free field realization of the affine…

Free Field Realizations of Induced Modules for Affine Lie Algebras

- Mathematics
- 2014

We construct a free field realization of generalized loop modules induced from admissible diagonal ℤ-graded irreducible modules of nonzero level for a Heisenberg subalgebra of untwisted affine Lie…

A Wakimoto type realization of toroidal $\mathfrak{sl}_{n+1}$

- Mathematics
- 2010

The authors construct a Wakimoto type realization of toroidal $\mathfrak{sl}_{n+1}$ The representation constructed in this paper utilizes non-commuting differential operators acting on the tensor…

Virasoro Action on Imaginary Verma Modules and the Operator Form of the KZ-Equation

- Mathematics
- 2012

We define the Virasoro algebra action on imaginary Verma modules for affine $${\mathfrak{sl}(2)}$$ and construct an analogue of the Knizhnik–Zamolodchikov equation in the operator form. Both these…

REALIZATIONS OF THE FOUR POINT AFFINE LIE ALGEBRA

- Mathematics
- 2008

We construct free field realizations of the four point algebra sl(2, R) ⊕ ((R /d R), where R = [ރt, t −1 , u | u 2 = t 2 − 2bt + 1].

Realizations of the three-point Lie algebra sl(2,ℛ) ⊕ (Ωℛ∕dℛ)

- Mathematics
- 2014

We describe the universal central extension of the three point current algebra $\mathfrak{sl}(2,\mathcal R)$ where $\mathcal R=\mathbb C[t,t^{-1},u\,|\,u^2=t^2+4t ]$ and construct realizations of it…

## References

SHOWING 1-10 OF 52 REFERENCES

Intermediate Wakimoto modules for affine

- Mathematics
- 2003

We construct certain boson-type realizations of affine that depend on a parameter 0 ≤ r ≤ n such that when r = 0 we get a Fock space realization appearing in [6] and when r = n they are the Wakimoto…

Intermediate Wakimoto modules for affine sl ( n + 1 , C )

- Mathematics
- 2004

We construct certain boson-type realizations of affine sl(n + 1, C) that depend on a parameter 0 r n such that when r = 0 we get a Fock space realization appearing in [6] and when r = n they are the…

Twisted Verma Modules

- Mathematics
- 2003

Using principal series Harish-Chandra modules, local cohomology with support in Schubert cells and twisting functors we construct certain modules parametrized by the Weyl group and a highest weight…

A new class of unitarizable highest weight representations of infinite-dimensional Lie algebras, II

- Mathematics
- 1989

Imaginary Verma Modules for Affine Lie Algebras

- MathematicsCanadian Mathematical Bulletin
- 1994

Abstract We study a class of irreducible modules for Affine Lie algebras which possess weight spaces of both finite and infinite dimensions. These modules appear as the quotients of "imaginary Verma…

Fock representations and BRST cohomology inSL(2) current algebra

- Mathematics
- 1990

We investigate the structure of the Fock modules overA1(1) introduced by Wakimoto. We show that irreducible highest weight modules arise as degree zero cohomology groups in a BRST-like complex of…

Borel Subalgebras and Categories of Highest Weight Modules for Toroidal Lie Algebras

- Mathematics
- 2001

Abstract In this article we begin an investigation of the conjugacy classes of Borel subalgebras together with Verma modules induced from “standard” Borel subalgebras of a toroidal Lie algebra t in…

Semi-infinite induction and Wakimoto modules

- Mathematics
- 1997

The purpose of this paper is to suggest the construction and study properties of semi-infinite induction, which relates to semi-infinite cohomology the same way induction relates to homology and…

Free field realization of SL(2) correlators for admissible representations, and hamiltonian reduction for correlators

- Mathematics
- 1995

Affine Kac-Moody algebras and semi-infinite flag manifolds

- Mathematics
- 1990

We study representations of affine Kac-Moody algebras from a geometric point of view. It is shown that Wakimoto modules introduced in [18], which are important in conformal field theory, correspond…