letterio.gatto@polito.it
Let $V=\mathbb{Q}[X]$ be the vector space of polynomials with rational coefficients. The purpose of the talk will be to show how the exterior algebra $\wedge V$ is a representation of the Lie algebra of the endomorphisms of $V$ (via ''traces'') as well as of the ring of symmetric functions (symmetric ''polynomials'' in infinitely many indeterminates) over the rationals. These two occurrences have relationships with a number of classical and less classical subjects, such as a substantial generalization of the Cayley-Hamilton theorem, working also for countable infinite dimensional spaces, and/or with Schubert calculus on Grassmannians and/or, again, with the vertex operators attached to the boson-fermion correspondence. The talk is thought to be given to a general audience and the choice of the expository path will be shaped on its general background.
(Esta charla pertenece al programa del Seminario del IMUS, que la financia. Expuesta aquí a título informativo.)