Simply-Laced Quantum Connections Generalising KZ

Bmw Algebras of Simply Laced Type

It is known that the recently discovered representations of the Artin groups of type An, the braid groups, can be constructed via BMW algebras. We introduce similar algebras of type Dn and En which also lead to the newly found faithful representations of the Artin groups of the corresponding types. We establish finite dimensionality of these algebras. Moreover, they have ideals I1 and I2 with I...

Brauer Algebras of Simply Laced Type

The diagram algebra introduced by Brauer that describes the centralizer algebra of the n-fold tensor product of the natural representation of an orthogonal Lie group has a presentation by generators and relations that only depends on the path graph An−1 on n− 1 nodes. Here we describe an algebra depending on an arbitrary graph M , called the Brauer algebra of type M , and study its structure in...

Duality for nonlinear simply laced groups

We establish a character multiplicity duality for a certain natural class of nonlinear (nonalgebraic) groups arising as two-fold covers of simply laced real reductive algebraic groups. This allows us to extend part of the formalism of the Local Langlands Conjecture to such groups.

A Local Characterization of Simply-Laced Crystals

Dorey’s Rule and the q-Characters of Simply-Laced Quantum Affine Algebras

Let Uq(ĝ) be the quantum affine algebra associated to a simply-laced simple Lie algebra g. We examine the relationship between Dorey’s rule, which is a geometrical statement about Coxeter orbits of g-weights, and the structure of q-characters of fundamental representations Vi,a of Uq(ĝ). In particular, we prove, without recourse to the ADE classification, that the rule provides a necessary and ...