"A Super Quantum Lie Day"

poster: Affine Supergroups vs. Super Harish-Chandra Pairs

speaker: Fabio Gavarini (Università di Roma "Tor Vergata" - Dipartimento di Matematica)

abstract: I present a new method to associate a "split" affine supergroup with any super Harish-Chandra pair (=sHCp), that provides an equivalence of categories between sHCp's and (split) affine supergroups. Namely, I provide a new functorial construction that, with each super Harish-Chandra pair, associates a split affine supergroup: this functor is then proved to be a quasi-inverse to the natural functor from (split) affine supergroups to super Harish-Chandra pairs, so the two yield equivalences between the corresponding categories. The existence of similar equivalences was known (possibly in different contexts, such as the smooth or the complex analytic one), but the construction I present is actually new - the quasi-inverse functor that I introduce is different - and extends the result to a much larger setup, with a totally different, more geometrical method.

Reference: arXiv:1308.0462, to appear in "Transactions of the AMS"

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