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Paper detail

Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras

We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in noncommuting variables. Each is a Hopf algebra and the two are isomorphic as such. This allows developments in each to be transferred. The identification suggests a rich class of examples for the emerging field of combinatorial Hopf algebras.

preprint2011arXivOpen access
Marcelo AguiarCarlos AndreCarolina BenedettiNantel BergeronZhi ChenPersi DiaconisAnders HendricksonSamuel HsiaoI. Martin IsaacsAndrea JedwabKenneth JohnsonGizem KaraaliAaron LauveTung LeStephen LewisHuilan LiKay MagaardEric MarbergJean-Christophe NovelliAmy PangFranco SaliolaLenny TevlinJean-Yves ThibonNathaniel ThiemVidya VenkateswaranC. Ryan VinrootNing YanMike Zabrocki
math.COmath.RT
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Marcelo AguiarCarlos AndreCarolina BenedettiNantel BergeronZhi ChenPersi DiaconisAnders HendricksonSamuel HsiaoI. Martin IsaacsAndrea JedwabKenneth JohnsonGizem KaraaliAaron LauveTung LeStephen LewisHuilan LiKay MagaardEric MarbergJean-Christophe NovelliAmy PangFranco SaliolaLenny TevlinJean-Yves ThibonNathaniel ThiemVidya VenkateswaranC. Ryan VinrootNing YanMike Zabrocki

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