Algebra Seminar: Strayer -- Minuscule Lie theory via colored posets

Michael C. Strayer (Hampden-Sydney College) will be speaking in the algebra seminar.  We
will go out for lunch after the talk---all are welcome to join! 

When: 12-1pm Friday June 12 

Where: SMRI Seminar Room (Macleay Building A12 Room 301) 

Title: Minuscule Lie theory via colored posets 

Abstract: The well-known minuscule representations of simple Lie algebras are
irreducible highest weight representations whose weights consist of a single Weyl group
orbit. In this talk we will discuss ways to generalize the essential "minuscule"
properties of these representations to include highest weight and non-highest weight
representations, Kac--Moody and positive Borel representations, and finite and infinite
dimensional representations. We will also discuss the dominant $\lambda$-minuscule
Weyl group elements of D. Peterson. Each setting uses a construction of a partially
ordered set that has been "colored" by the nodes of the associated Dynkin diagram. We
will display examples in finite, affine, and indefinite types. We also show how to
produce a concrete combinatorial basis for a representation isomorphic to $V(m\lambda)$,
the irreducible highest weight representation of highest weight $m\lambda$, where
$\lambda$ is one of the classic minuscule weights in finite type. This basis is
indexed by $m$-multichains in the weight lattice of $V(\lambda)$ and is over the
integers in a certain fashion.