2019/02/11 by Gatto, Letterio, Salehyan, Parham
#14M15 #15A75 #17B69 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1902.03824
The integral singular cohomology ring of the Grassmann variety parametrizing r-dimensional subspaces in the n-dimensional complex vector space is naturally an irreducible representation of the Lie algebra of all the n× n matrices with integral entries. Using the notion of Schubert derivation, a distinguished Hasse-Schmidt derivation on an exterior algebra, we describe explicitly such a representation, indicating its relationship with the celebrated bosonic vertex representation of the Lie algebra of infinite matrices due to Date, Jimbo, Kashiwara and Miwa.