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On cubes of Frobenius extensions. (English) Zbl 1369.19003

Krause, Henning (ed.) et al., Representation theory – Current trends and perspectives. In part based on talks given at the last joint meeting of the priority program in Bad Honnef, Germany, in March 2015. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-171-2/hbk; 978-3-03719-671-7/ebook). EMS Series of Congress Reports, 171-186 (2017).
Summary: Given a hypercube of Frobenius extensions between commutative algebras, we provide a diagrammatic description of some natural transformations between compositions of induction and restriction functors, in terms of colored transversely-intersecting planar 1-manifolds. The relations arise in the first and third author’s work on (singular) Soergel bimodules.
For the entire collection see [Zbl 1357.14004].

MSC:

19A22 Frobenius induction, Burnside and representation rings
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
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