Geometric Langlands duality and forms of reductive groups

2008/11/17 by Dhand, Vivek
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.0811.2620

Abstract

The category of perverse sheaves on the affine Grassmannian of a complex reductive group G gives a canonical geometric construction of the split form of the Langlands dual group \check G_\bZ over the integers. Given a field k, we give a Tannakian construction of the quasi-split forms of \check G_k, as well as a construction of the gerbe associated to an inner form of \check G_k.

Related

• Geometric Langlands duality and representations of algebraic groups over commutative rings
• Perverse Sheaves on affine Grassmannians and Langlands Duality
• Perverse Sheaves on Loop Grassmannians and Langlands Duality
• Perverse sheaves on a Loop group and Langlands' duality
• Perverse Sheaves on Real Loop Grassmannians