Algebraic Combinatorics Lecture Notes

Overview & Synopsis

This book
explains the following topics, Diagram Algebras and Hopf Algebras, Group
Representations, SnRepresentations Intro, Decomposition and Specht
Modules, Fundamental Specht Module Properties and Branching Rules,
Representation Ring for Sn and its Pieri Formula, Pieri for Schurs, Kostka
Numbers, Dual Bases, Cauchy Identity, Finishing Cauchy, LittlewoodRichardson
Rule, Frobenius Characteristic Map, Algebras and Coalgebras, Skew Schur
Functions and Comultiplication, Sweedler Notation, kCoalgebra Homomorphisms,
Subcoalgebras, Coideals, Bialgebras, Bialgebra Examples, Hopf Algebras Defined,
Properties of Antipodes and Takeuchis Formula, etc.