Projective representations of the braid group of the torus and representations of the double affine Hecke algebra are obtained.doi:10.1007/bf02099981Pavel I. EtingofCommunications in Mathematical PhysicsP. I. Etingof, Representations of affine Lie algebras, elliptic r-matrix systems, and special ...
We give an explicit description of the Kac-Peterson-Lepowsky construction of the basic representation for the affine Lie algebraB n (1). Using the conjugacy classes of the Weyl group ofB n, we describe all inequivalent maximal Heisenberg subalgebras of the corresponding affine Lie algebra. We ...
Journal of Functional AnalysisTwo constructions of affine Lie algebra representations and boson-fermion correspondence in quantum field theory - Frenkel - 1981Frenkel, I.B.: Two constructions of affine Lie algebra represntations and boson- fermion correspondence in quantum field theory. J. Funct. ...
The aim of this note is to show that the affine Lie algebraA 1 (1) has a natural family πμ, υ,v of Fock representations on the spaceC[x i,y
The module structure is defined on the vector space tensor product of the fundamental representations of the quantum affine algebra. To do this, we find a particular basis of every fundamental representation, consisting of eigenvectors for some of the Drinfeld generators of the algebra. The tensor ...
Representations of affine Lie algebras, parabolic differential\n equations, and Lame functions We consider correlation functions for the Wess-Zumino-Witten model on the torus with the insertion of a Cartan element; mathematically this means that we c... P Etingof,A Kirillov Jr - 《Duke Mathematica...
arXiv:107.1118v1[math.RT]3Jul01AdmissiblerepresentationsofsimpleaffinevertexalgebrasVyacheslavFutornyOscarArmandoHernándezMoralesLiborKřižkaAbstractWeprovideanexplicitcombinatorialdescriptionofhighestweightsofsimplehighestweightmodulesoverthesimpl
We construct vertex representations of quantum affine algebras of ADE type, which were first introduced in greater generality of Drinfeld and Jimbo. The limiting special case of our construction is the untwisted vertex representation of affine Lie algebras of Frenkel-Kac and Segal. Our representation...
T. Arakawa, Characters of representations of affine Kac-Moody Lie algebras at the critical level, arXiv:0706.1817v2 [math.QA].T. Arakawa, Characters of representations of affine Kac-Moody Lie algebras at the critical level, arXiv:0706.1817....
The quantum Drinfeld–Sokolov reduction transforms the representations of the affine Lie algebras into their W-algebra counterparts, and can be used to produce analogues of the modified regular representations. When g=sl(2,C) the corresponding W-algebra is the Virasoro algebra. We describe the Vira...