Braid Group Action and Canonical Bases

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 ...

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...

Canonical Bases and the Conjugating Representation of a Semisimple Group

We fix an algebraically closed field k of characteristic zero. Let G be a reductive affine algebraic group over k and let V be an affine G-variety over k. We denote by A(G) and A(V ) the k-algebras of regular functions on G and V respectively. The action of G on V gives rise to a rational representation of G on A(V ). A natural question is to investigate whether the algebra A(V ) is a free modu...

Categorical Affine Braid Group Action on Springer Resolutions