Representation Theory and Mathematical Physics Seminar: Vertex operators realizations of families of symmetric functions

Seminar | April 30 | 4-5 p.m. | 748 Evans Hall

 Natalia Rojkovskaia, Kansas State University

 Department of Mathematics

The algebra of charged free fermions participates in the construction of classical boson-fermion correspondence and provides vertex operator realization of Schur symmetric functions. We will show how vertex operator realizations of several other famous families of symmetric functions (Hall-Littlewood polynomials, shifted Schur functions, multiparameter Schur Q-functions) can be obtained by simple modifications of operators of charged free fermions and make some notes on the corresponding versions of boson-fermion correspondence.