Pure Maths Colloquium: Boson-fermion correspondence in combinatorics and representation theory
8 May 2017 16:00 in CM221
Boson-fermion correspondence is an isomorphism between symmetric polynomials of even variables and antisymmetric polynomials of odd variables. This isomorphism holds of course only if the number of variables is infinite. It can be described just by drawing nice
diagrams and allows to give an elementary approach to several combinatorial constructions. As an example we will consider the Jacobi triple product identity, relations between Newton and Schur polynomials and computations of characters of the symmetric group with paper and pencil. We will also sketch a recent application of this correspondence by Don Zagier to the proof of Bloch-Okounkov theorem claiming that certain sums over partitions give quasimodular forms.
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