Join us for an upcoming seminar featuring mathematics faculty and invited speakers on one of our seven research topics. You may also see upcoming seminars by topic:
Type C combinatorics of two-pole centralizer algebras
Speaker: Zajj Daugherty
Hecke algebras arise in one sense as deformations of Weyl groups, but in another sense as quotients of braid algebras. While some types of braid algebras can only loosely be associated to their namesake, some can be concretely imagined as braid diagrams on k strands, possibly in spaces with one or more punctures. The latter produces a connection to quantum group actions on tensor spaces of particular shapes. For example, the finite Hecke algebra of type A has a natural action on a tensor space V^{\otimes k}, which commutes with the natural action of the quantum group of type A (this is precisely the q-deformation of classical Schur-Weyl duality). Closures of braids then correspond to traces of endomorphisms, giving rise to knot and link invariants via Hecke algebras; actions on tensor space have implications for lattice models in statistical mechanics; and on the connections go. Read more.