3 research outputs found
Representations of Lie algebras arising from polytopes
We present an extremely elementary construction of the simple Lie algebras
over the complex numbers in all of their minuscule representations, using the
vertices of various polytopes. The construction itself requires no complicated
combinatorics and essentially no Lie theory other than the definition of a Lie
algebra; in fact, the Lie algebras themselves appear as by-products of the
construction.Comment: Approximately 32 pages, AMSTe
On triangles with a minuscule side
Let be the Weyl group of a root system . If
with , and respectively conjugated to ,
and in V , then is conjugated to in when each
projection of to an irreducible component of is co-linear to a
minuscule coweight.Comment: in Frenc
Exceptional Theta-correspondences I
Let be a split simply laced group defined over a -adic field . In
this paper we study the restriction of the minimal representation of to
various dual pairs in . For example, the restriction of the minimal
representation of to the dual pair Sp(6) gives the
non-endoscopic Langlands lift of irreducible representations of to Sp(6)