The Hopf algebra of symmetric functions in noncommuting variables NCSym(X) has an representation theoretic realization as a space of supercharacters of the finite unipotent upper-triangular matrices. In such a correspondence, the representation theory gives several distinguished sets of bases for NCSym(X). However, it is also natural to ask whether we learn anything about supercharacters from such a correspondence. This talk gives one possible answer to such a question, demonstrating how an obvious basis of NCSym(X) has a surprising representation theoretic interpretation on supercharacters. This is joint work with N. Bergeron.
Symmetric functions and the representation theory of unipotent upper-triangular matrices
Symmetric functions and the representation theory of unipotent upper-triangular matrices