A now classical method to construct the Schur functions is constructing matrix el- ements using half vertex operators associated to the classical boson-fermion cor- respondence. This construction is known as using free fermions. Schur functions are also known to be polynomial representatives of cohomology classes of Schu- bert varieties in the Grassmannian. By instead using K-theory, the representatives become the (symmetric) Grothendieck polynomials. A recent generalization was given by Hwang et al. called the (refined) canonical Grothendieck polynomials based on the work of Galashin–Grinberg–Liu and Yeliussizov. In this talk, we take the Jacobi–Trudi formulas of Hwang et al. as our definition and use Wick’s theorem to give a presentation for the canonical Grothendieck polynomials and their dual basis using free fermions. This generalizing the recent work of Iwao. Using this, we derive many known identities, as well as some new ones, through simple computations. This is based on joint work with Shinsuke Iwao and Kohei Motegi (arXiv: 2211.05002).
By Paul-André Melliès
By Paul-André Melliès
By Cyril Banderier
By Sergey Yurkevich
By Karol Penson
By Frédéric Patras
By Darij Grinberg
By Travis Scrimshaw
By Arthemy Kiselev
By Béa de Laporte
By Viviane Pons
By Gérard Ben Arous
By Viviane Pons
By Wenjie Fang
By Misha Gromov
By Céline Duval
By Olivier Benoist
