Abstract
We give a bijection between certain colored partitions and the elements in the quotient of an affine Weyl group modulo its Weyl group. By Bott's formula these colored partitions give rise to some partition identities. In certain types, these identities have previously appeared in the work of Bousquet-Melou-Eriksson, Eriksson-Eriksson and Reiner. In other types the identities appear to be new. Our main application is to determine the rationally smooth Schubert varieties in the affine Grassmannians. Several of the proofs are computer assisted. This is joint work with Steve Mitchell.
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