scholarly journals The Deformed Virasoro Algebra at Roots of Unity

1998 ◽  
Vol 196 (2) ◽  
pp. 249-288 ◽  
Author(s):  
Peter Bouwknegt ◽  
Krzysztof Pilch
Keyword(s):  
Virasoro Algebra ◽  
Roots Of Unity ◽  
Deformed Virasoro Algebra

A (p,q)-deformed Virasoro algebra

1992 ◽  
Vol 25 (9) ◽  
pp. 2607-2614 ◽  
Author(s):  
R Chakrabarti ◽  
R Jagannathan
Keyword(s):  
Virasoro Algebra ◽  
Deformed Virasoro Algebra

scholarly journals A QUADRATIC DEFORMATION OF THE HEISENBERG–WEYL AND QUANTUM OSCILLATOR ENVELOPING ALGEBRAS

1993 ◽  
Vol 08 (20) ◽  
pp. 3479-3493 ◽  
Author(s):  
JENS U. H. PETERSEN
Keyword(s):  
Virasoro Algebra ◽  
Heisenberg Algebra ◽  
Roots Of Unity ◽  
Quantum Oscillator ◽  
Dimensional Representation ◽  
Finite Dimensional Representation ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Quadratic Deformation ◽  
Two Parameter

A new two-parameter quadratic deformation of the quantum oscillator algebra and its one-parameter deformed Heisenberg subalgebra are considered. An infinite-dimensional Fock module representation is presented, which at roots of unity contains singular vectors and so is reducible to a finite-dimensional representation. The semicyclic, nilpotent and unitary representations are discussed. Witten's deformation of sl 2 and some deformed infinite-dimensional algebras are constructed from the 1d Heisenberg algebra generators. The deformation of the centerless Virasoro algebra at roots of unity is mentioned. Finally the SL q(2) symmetry of the deformed Heisenberg algebra is explicitly constructed.

scholarly journals A note on the deformed Virasoro algebra

1996 ◽  
Vol 367 (1-4) ◽  
pp. 121-125 ◽  
Author(s):  
Sergei Lukyanov
Keyword(s):  
Virasoro Algebra ◽  
Deformed Virasoro Algebra

scholarly journals Lattice models, deformed Virasoro algebra and reduction equation

2020 ◽  
Vol 53 (24) ◽  
pp. 245202
Author(s):  
Michael Lashkevich ◽  
Yaroslav Pugai ◽  
Jun’ichi Shiraishi ◽  
Yohei Tutiya
Keyword(s):  
Lattice Models ◽  
Virasoro Algebra ◽  
Reduction Equation ◽  
Deformed Virasoro Algebra

scholarly journals FREE FIELD CONSTRUCTIONS FOR THE ELLIPTIC ALGEBRA $\rscr{A}_{q,p}(\widehat{sl}_2)$ AND BAXTER'S EIGHT-VERTEX MODEL

2004 ◽  
Vol 19 (supp02) ◽  
pp. 363-380 ◽  
Author(s):  
J. SHIRAISHI
Keyword(s):  
Integral Formula ◽  
Free Field ◽  
Virasoro Algebra ◽  
Vertex Operators ◽  
Vertex Model ◽  
Elliptic Algebra ◽  
Deformed Virasoro Algebra ◽  
The One ◽  
Level 2 ◽  
Elliptic Quantum

Three examples of free field constructions for the vertex operators of the elliptic quantum group [Formula: see text] are obtained. Two of these ( for p1/2=±q3/2, p1/2=-q2) are based on representation theories of the deformed Virasoro algebra, which correspond to the level 4 and level 2 Z-algebra of Lepowsky and Wilson. The third one (p1/2=q3) is constructed over a tensor product of a bosonic and a fermionic Fock spaces. The algebraic structure at (p1/2=q3), however, is not related to the deformed Virasoro algebra. Using these free field constructions, an integral formula for the correlation functions of Baxter's eight-vertex model is obtained. This formula shows different structure compared with the one obtained by Lashkevich and Pugai.

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