Quantum Supergroups V. Braid Group Action

Braid Group Action and Quantum Affine Algebras

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 Drinfel ′ d's new realization. Coproduct formulas are given and a PBW type basis is constructed. §0. Introduction. The purpose of this pape...

On a Braid Group Action

We discuss some consequences of the braid group action on a categorified quantum group. Results include a description of reflection functors for quiver Hecke algebras and a theory of restricting categorical representations along a face.

The Hurwitz Action and Braid Group Orderings

In connection with the so-called Hurwitz action of homeomorphisms in ramified covers we define a groupoid, which we call a ramification groupoid of the 2sphere, constructed as a certain path groupoid of the universal ramified cover of the 2-sphere with finitely many marked-points. Our approach to ramified covers is based on cosheaf spaces, which are closely related to Fox’s complete spreads. A ...

Quantum automata, braid group and link polynomials

The spin–network quantum simulator model, which essentially encodes the (quantum deformed) SU(2) Racah–Wigner tensor algebra, is particularly suitable to address problems arising in low dimensional topology and group theory. In this combinatorial framework we implement families of finite–states and discrete–time quantum automata capable of accepting the language generated by the braid group, an...

Categorical Affine Braid Group Action on Springer Resolutions