Braid Group Action and Quantum Affine Algebras
Jonathan Beck
TL;DR
This paper introduces a braid group action on quantum affine algebras that preserves the Heisenberg subalgebra, constructs loop generators satisfying Drinfeld's relations, and provides coproduct formulas and a PBW basis.
Contribution
It extends the affine Weyl group lattice to a braid group action on quantum affine algebras, revealing new structural insights.
Findings
Braid group action fixes the Heisenberg subalgebra pointwise
Loop generators satisfying Drinfeld's relations are constructed
Coproduct formulas and a PBW basis are established
Abstract
We lift the lattice of translations in the extended affine Weyl group to a braid group action on the quantum affine algebra. This action fixes the Heisenberg subalgebra pointwise. Loop like generators are found for the algebra which satisfy the relations of Drinfeld's new realization. Coproduct formulas are given and a PBW type basis is constructed.
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