BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Letterio Gatto (Politecnico di Torino) DTSTART:20210630T183000Z DTEND:20210630T200000Z DTSTAMP:20260423T021727Z UID:BRAG/53 DESCRIPTION:Title: On the Vertex Operators Representation of Lie Algebras of Matrices\nby L etterio Gatto (Politecnico di Torino) as part of Brazilian algebraic geome try seminar\n\n\nAbstract\nRelying on our common skill to multiply square matrices by vectors\, recalled in the first part of the talk\, we will des cribe the exterior algebra of a polynomial ring in one indeterminate\, and /or the ring of symmetric polynomials\, as a representation of the Lie alg ebra of matrices of infinite size with all but finitely many zero entries. \n\nThe description is achieved by bridging classical Schubert calculus on Grassmannians to the vertex operators occurring in the so-called boson-fe rmion correspondence (Poincaré duality for Grassmannians of infinite dime nsional linear spaces) and highlights a substantial generalization of a cl assical picture drawn in the Eighties by Date\, Jimbo\, Kashiwara and Miwa \, within the framework of algebraic analysis and infinite dimensional com pletely integrable systems. The talk will survey joint work with (in alpha betical order) O. Behzad\, A. Contiero\, D. Martins\, P. Salehyan\, I. Sch erbak and R. Vidal Martins.\n LOCATION:https://researchseminars.org/talk/BRAG/53/ END:VEVENT END:VCALENDAR