Lattice $W$ algebras and quantum groups

Details Lattice $W$ algebras and quantum groups Lattice $W$ algebras and quantum groups

1993-07-20

arxiv.org/abs/hep-th/9307127v2

Theor.Math.Phys. 100 (1994) 900-911; Teor.Mat.Fiz. 100 (1994) 132-147

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, misprints have been corrected

Scientific paper

10.1007/BF01017329

We represent Feigin's construction [22] of lattice W algebras and give some simple results: lattice Virasoro and $W_3$ algebras. For simplest case $g=sl(2)$ we introduce whole $U_q(sl(2))$ quantum group on this lattice. We find simplest two-dimensional module as well as exchange relations and define lattice Virasoro algebra as algebra of invariants of $U_q(sl(2))$. Another generalization is connected with lattice integrals of motion as the invariants of quantum affine group $U_q(\hat{n}_{+})$. We show that Volkov's scheme leads to the system of difference equations for the function from non-commutative variables.

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