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한국고등과학원 세미나 



An introduction to quasisymmetric functions, Schur functions and their intersection I 

van Willigenburg, Stephanie (University of British Columbia ) 
In algebraic combinatorics, a central area of study is Schur functions. These functions were introduced early in the last century with respect to representation theory, and since then have become important in other areas such as quantum physics and algebraic geometry. These functions also form a basis for the algebra of symmetric functions, which is a subalgebra of the algebra of quasisymmetric functions that appear in areas such as category theory and card shuffling. Despite this strong connection, the existence of a natural quasisymmetric refinement of Schur functions was considered unlikely for many years. In this short course we will introduce quasisymmetric functions and Schur functions. Then we will introduce quasisymmetric Schur functions. We will see how these quasisymmetric Schur functions refine Schur function properties, with combinatorics that strongly reflects the classical case such as diagrams. This course needs no knowledge of any of the above terms. Everything will be defined, and illustrated with examples. 







