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arXiv · hep-th/9307127

Lattice $W$ algebras and quantum groups

Ya. P. Pugay
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Abstract

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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Ya. P. Pugay. 1993-08-21. Lattice $W$ algebras and quantum groups. https://doi.org/10.1007/bf01017329

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