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A categorification of the Malvenuto-Reutenauer algebra via a tower of groups

Farid Aliniaeifard, The University of British Columbia
Wednesday, February 3, 2021 - 3:30pm to 5:00pm
via Zoom

Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.

Join Zoom Meeting:
Meeting ID: 915 4733 5974

There is a long tradition of categorifying combinatorial Hopf algebras by the modules of a tower of algebras (or even better via the representation theory of a tower of groups). From the point of view of combinatorics, such a categorification supplies canonical bases, inner products, and a natural avenue to prove positivity results. Recent ideas in supercharacter theory have made fashioning the representation theory of a tower of groups into a Hopf structure more tractable. As a demonstration, this talk reports on the results of the following challenge: (1) Pick a well-known combinatorial Hopf algebra, (2) Find a way to categorify the structure via a tower of groups. In this case, we show how to find the Malvenuto Reutenauer Hopf algebra in the representation theory of a tower of elementary abelian p-groups (with Nat Thiem).