Applies chiral cluster seeds to deformed W-algebras, introduces W_{q,t}^sub(sl(N)), and constructs embeddings viewed as deformed inverse quantum Hamiltonian reduction.
Drinfeld-Sokolov reduction for difference operators and deformations of W-algebras I. The case of Virasoro algebra
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We propose a q-difference version of the Drinfeld-Sokolov reduction scheme, which gives us q-deformations of the classical W-algebras by reduction from Poisson-Lie loop groups. We consider in detail the case of SL(2). The nontrivial consistency conditions fix the choice of the classical r-matrix defining the Poisson-Lie structure on the loop group LSL(2), and this leads to a new elliptic classical r-matrix. The reduced Poisson algebra coincides with the deformation of the classical Virasoro algebra previously defined in q-alg/9505025. We also consider a discrete analogue of this Poisson algebra. In the second part (q-alg/9702016) the construction is generalized to the case of an arbitrary semisimple Lie algebra.
fields
math.QA 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Deformed W-algebras and chiralized cluster seeds: subregular W-algebras and Inverse Quantum Hamiltonian Reduction
Applies chiral cluster seeds to deformed W-algebras, introduces W_{q,t}^sub(sl(N)), and constructs embeddings viewed as deformed inverse quantum Hamiltonian reduction.