2014/09/11 by Uma, V.
#14L10 #14M25 #14M27 #19L47 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1409.3467
In this article we describe the \tG× \tG-equivariant K-ring of X, where \tG is a \it factorial cover of a connected complex reductive algebraic group G, and X is a regular compactification of G. Furthermore, using the description of K\tG× \tG(X), we describe the ordinary K-ring K(X) as a free module of rank the cardinality of the Weyl group, over the K-ring of a toric bundle over G/B, with fibre the toric variety T+, associated to a smooth subdivision of the positive Weyl chamber. This generalizes our previous work on the wonderful compactification (see \citeu). Further, we give an explicit presentation of K\tG× \tG(X) as well as K(X) as an algebra over the K\tG× \tG(Gad) and K(Gad) respectively, where Gad is the wonderful compactification of the adjoint semisimple group Gad. Finally, we identify the equivariant and ordinary Grothendieck ring of X respectively with the corresponding rings of a canonical toric bundle over Gad with fiber the toric variety T+.