Hopf Algebras in Combinatorics

A ug 2 00 9 SKEW LITTLEWOOD - RICHARDSON RULES FROM HOPF ALGEBRAS

Assaf and McNamara [1] recently used combinatorics to give an elegant and surprising formula for the product of a skew Schur function by a complete homogeneous symmetric function. Their paper included an appendix by one of us (Lam) with a simple algebraic proof of their formula, and also a conjectural skew version of the Littlewood-Richardson rule. We show how these formulas and much more are s...

Hopf Algebras in General and in Combinatorial Physics: a practical introduction

This tutorial is intended to give an accessible introduction to Hopf algebras. The mathematical context is that of representation theory, and we also illustrate the structures with examples taken from combinatorics and quantum physics, showing that in this latter case the axioms of Hopf algebra arise naturally. The text contains many exercises, some taken from physics, aimed at expanding and ex...

Coalgebras, Hopf Algebras and Combinatorics

In loving memory of my mother " A mathematician is a machine for converting coffee into theorems. " —Alfréd Rényi " A comathematician, by categorical duality, is a machine for converting cotheorems into ffee. " —anonymous Preface Hopf algebras are a relatively new concept in algebra, first encountered by their namesake Heinz Hopf in 1941 in the field of algebraic topology. In the 1960s, study o...

NOTES ON REGULAR MULTIPLIER HOPF ALGEBRAS

In this paper, we associate canonically a precyclic mod- ule to a regular multiplier Hopf algebra endowed with a group-like projection and a modular pair in involution satisfying certain con- dition

On the Coderivations of Some Hopf Algebras