Canonical Grothendieck Polynomials with Free Fermions

Explore a lecture on constructing canonical Grothendieck polynomials using free fermions. Delve into the classical method of constructing Schur functions through matrix elements and half vertex operators associated with the boson-fermion correspondence. Examine the connection between Schur functions and cohomology classes of Schubert varieties in the Grassmannian, and learn how K-theory leads to symmetric Grothendieck polynomials. Investigate the recent generalization of refined canonical Grothendieck polynomials by Hwang et al., based on work by Galashin–Grinberg–Liu and Yeliussizov. Discover how Wick's theorem is applied to derive a presentation for canonical Grothendieck polynomials and their dual basis using free fermions, extending Iwao's recent work. Gain insights into known identities and new findings through simple computations based on joint research with Shinsuke Iwao and Kohei Motegi.