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S. Kleiman:
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2015

A K_T-deformation of the ring of symmetric functions

Knutson, Allen, Lederer, Mathias

Understand

The ring of symmetric functions can be implemented in the homology of \union_{a,b} Gr(a,a+b), the multiplicative structure being defined from the "direct sum" map.

There is a natural circle action (simultaneously on all Grassmannians) under which each direct sum map is equivariant.
Upon replacing usual homology by equivariant K-homology, we obtain a 2-parameter deformation of the ring of symmetric functions.
This ring has a module basis given by Schubert classes.