Matrix symmetric and quasi-symmetric functions

Abstract: A fundamental result by L. Solomon states that formulas for the computation of tensor products of symmetric group representations can be lifted to the corresponding (Solomon’s) descent algebra, a subalgebra of the group algebra with a very rich structure. Motivated by the structure of the product formula in these algebras and by other results and ideas in the field, we introduce and investigate a two dimensional analog based on packed integer matrices that inherits most of their fundamental properties. One of the structures we introduce identifies with a bialgebra recently introduced by J. Diehl and L. Schmitz to define a two dimensional generalisation of Chen’s iterated integrals signatures. J.w. with L. Foissy and C. Malvenuto.

machine learningcommutative algebraalgebraic geometryalgebraic topologycombinatoricscategory theoryoperator algebrasrings and algebrasrepresentation theory

Audience: researchers in the topic

( paper | video )

Algebraic and Combinatorial Perspectives in the Mathematical Sciences

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