A K_T-deformation of the ring of symmetric functions

摘要: The ring of symmetric functions can be implemented in the homology \union_{a,b} Gr(a,a+b), multiplicative structure being defined from "direct sum" map. There is a natural circle action (simultaneously on all Grassmannians) under which each direct sum map equivariant. Upon replacing usual by equivariant K-homology, we obtain 2-parameter deformation functions. This has module basis given Schubert classes. Geometric considerations show that multiplication classes positive coefficients, an appropriate sense. In this paper give manifestly formulae for these coefficients: they count numbers "DS pipe dreams'' with prescribed edge labelings.